Shade the Venn diagram to represent the set A' U (A ∩ B)

Shade the Venn diagram to represent the set A' U (A ∩ B)
MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) A B

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) First shade 𝑨∩𝑩. A B

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) First shade 𝑨∩𝑩. A B A ∩ B

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) Now add in the shading for 𝑨′. A B A ∩ B

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) Now add in the shading for 𝑨′. A B A ∩ B Recall that 𝐴′ is everything NOT in 𝐴.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) Now add in the shading for 𝑨′. A B A ∩ B A’ Recall that 𝐴′ is everything NOT in 𝐴.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) Now add in the shading for 𝑨′. A B A ∩ B A’ Recall that 𝐴′ is everything NOT in 𝐴. A’

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) And because the remaining set operation is U (union), the final shading is the combination of the two. A B A ∩ B A’ A’

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) And because the remaining set operation is U (union), the final shading is the combination of the two. A B

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Shade the Venn diagram to represent the set A' U (A ∩ B) A B

What regions make up X ∩ W' ∩ Y ?
MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ?

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′ And because the remaining set operation is ∩ (intersection), the final shading is the overlapping region (where the colors are blended).

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑟 7 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′ And because the remaining set operation is ∩ (intersection), the final shading is the overlapping region (where the colors are blended).

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 𝑟 7 What regions make up X ∩ W' ∩ Y ? For an intersection of multiple sets, the order does not matter. For that reason, it might be easier if we first rewrite the original expression so that we can save the complement, 𝑊′, for last. 𝑟 7 𝑋∩𝑊′∩𝑌≡(𝑋∩𝑌)∩𝑊′ And because the remaining set operation is ∩ (intersection), the final shading is the overlapping region (where the colors are blended).

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises
Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 A B U

Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 Begin with the innermost region. A B U

Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 Begin with the innermost region. A B 13 U

Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 =16 Begin with the innermost region. A B 13 3 + 𝑛 𝐴 =16 U

Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 Begin with the innermost region. A B 13 3 + 𝑛 𝐴 =16 U

Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 21= Begin with the innermost region. A B 13 3 + + 8 𝑛 𝐴 =16 𝑛 𝐵 =21 U

Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 Begin with the innermost region. A B 13 3 + + 8 𝑛 𝐴 =16 𝑛 𝐵 =21 U

Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 + 30 B A Begin with the innermost region. A B 13 3 + + 7 + 8 𝑛 𝐴 =16 𝑛 𝐵 =21 U 𝑛 𝐴′ =38

Use the given information to fill in the number of elements for each region in the Venn diagram below. n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38 + 30 Begin with the innermost region. A B 13 3 + + 8 𝑛 𝐴 =16 𝑛 𝐵 =21 U 𝑛 𝐴′ =38

Find the number of elements in each region below.
MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 B A U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 2 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A Continue with the other interior regions. 2 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 8 9 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises At this point, there are still 3 that are yet to be used. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is easiest. It tells us that there are 8 not in any of the 3 circles. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is easiest. It tells us that there are 8 not in any of the 3 circles. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 The blue shaded area is 𝐶′. 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 The yellow shaded area is 𝐴. 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 2 Move to the outer regions of the circles. 8 9 The region of blended colors represents the A∩𝐶′. 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one says that there are 28 in the overlap of 𝐶′ and 𝐴. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 21 2 Move to the outer regions of the circles. 8 9 The region of blended colors represents the A∩𝐶′. 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 21 2 Move to the outer regions of the circles. 8 9 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is straightforward. It tells us that there are 49 in circles A & B. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 Continue with the other interior regions. 21 2 Move to the outer regions of the circles. 8 9 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is straightforward. It tells us that there are 49 in circles A & B. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 + Continue with the other interior regions. ? 21 = 49 + + 2 Move to the outer regions of the circles. + 8 9 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises This one is straightforward. It tells us that there are 49 in circles A & B. Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 Begin with the innermost region. B A 7 + Continue with the other interior regions. 2 21 = 49 + + 2 Move to the outer regions of the circles. + 8 9 10 8 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in each region below. n(A ∩ B ∩ C) = n(C) = n(A ∩ C) = n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = n(A ∩ B) = n(B ∩ C) = n(A∪B) = 49 B A 7 2 21 2 8 9 10 8 U C

Find the number of elements in sets A, B & C if:
MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 11 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 11 3 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 11 3 + 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 11 3 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 1 + 11 3 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 1 11 3 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 1 + + + 11 3 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 1 11 3 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 1 + + 19= + + + 11 3 + ? + 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 1 + + 19= + + + 11 3 + + 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B A 1 11 3 + U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B 𝑛 𝐴 = A 1 11 3 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B 𝑛 𝐴 =12 A 1 11 3 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 = 11 3 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 =3 11 3 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 =3 11 3 𝑛 𝐶 = 4 U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises Find the number of elements in sets A, B & C if: A ∩ B = Ø n(B ∩ C) = n(A ─ C) = n(U) = 19 n(A ∩ C) = n(C ─ A) = n(B ) = 3 B 𝑛 𝐴 =12 A 1 𝑛 𝐵 =3 11 3 𝑛 𝐶 =18 4 U C

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 𝑛 𝐴∪𝐷 = = 285

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). ∪ Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 𝐴 𝐷 111 80 31 29 10 24 152 133 𝑛 𝐴∪𝐷 = = 285

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). ∪ Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 𝐴 𝐷 111 80 + + 31 29 + + 10 24 152 133 𝑛 𝐴∪𝐷 = = 285

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). ∪ Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 𝐴 𝐷 285 111 80 + + 31 29 + + 10 24 152 133 𝑛 𝐴∪𝐷 = = 285

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 111 80 31 29 10 24 152 133

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 111 80 31 29 10 24 152 133 𝑛 𝐵∩𝐹 = 9

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 𝐵 111 54 80 𝐹 31 31 9 1 29 29 70 10 3 24 152 66 133 𝑛 𝐵∩𝐹 = 9

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 𝐵 111 111 54 80 80 𝐹 31 31 31 9 1 29 29 29 70 10 10 3 24 24 152 152 66 133 133 𝑛 𝐵∩𝐹 = 9

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 𝐵 111 111 54 80 80 𝐹 31 31 31 9 1 29 29 29 70 10 10 3 24 24 152 152 66 133 133 𝑛 𝐵∩𝐹 =9 9

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 9 𝐵 111 111 54 80 80 𝐹 31 31 31 9 1 29 29 29 70 10 10 3 24 24 152 152 66 133 133 𝑛 𝐵∩𝐹 =9 9

The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). The number of animals counted in wildlife observations of a certain watering hole are shown by class and time of highest activity (see table). Using the letters in the table, find n(A ∪ D) and n(B ⋂ F). Mammals (A) Birds (B) Reptiles (C) Fish (D) Total Morning (E) 111 54 6 80 251 Afternoon (F) 31 9 1 29 70 Evening (G) 10 3 48 24 85 152 66 55 133 406 285 9 𝐵 111 111 54 80 80 𝐹 31 31 31 9 1 29 29 29 70 10 10 3 24 24 152 152 66 133 133

92 cities were surveyed to determine sports teams.
MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 + ? Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 + 6 Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 6 Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 + ? 6 Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 + 5 6 Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. Begin with the innermost region. 7 5 6 Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. ? + Begin with the innermost region. 7 5 6 Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 + Begin with the innermost region. 7 5 6 Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 5 6 Continue with the other interior regions.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 5 6 Continue with the other interior regions. Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 + 5 + 6 Continue with the other interior regions. + ? Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 + 5 + 6 Continue with the other interior regions. + 1 Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 Begin with the innermost region. 7 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 ? + Begin with the innermost region. + 7 5 + 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 4 + Begin with the innermost region. + 7 5 + 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 4 Begin with the innermost region. 7 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 ? 4 + + Begin with the innermost region. 7 + 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + Begin with the innermost region. 7 + 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 6 4 Begin with the innermost region. 7 5 6 Continue with the other interior regions. 1 Move to the outer regions of the circles.

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + + 7 + 5 + 6 =35 + 1

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + 92 cities were surveyed + 7 + 5 + 6 =35 + 92 1

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + 92 cities were surveyed 35 cities had at least one + 7 + 5 + 6 =35 + 92 35 1

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + 92 cities were surveyed 35 cities had at least one + 7 + 5 + 6 =35 + 92 ― 35 1 = 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 6 4 + + 92 cities were surveyed 35 cities had at least one + 7 + 5 + 6 + 92 ― 35 1 57 = 57 57 cities had none of these

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball Fill in the number of elements in each region. 6 6 4 7 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had only volleyball? 6 6 4 7 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had only volleyball? 6 6 4 1 7 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer & rugby but not volleyball? 6 6 4 7 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer & rugby but not volleyball? 6 6 4 X 7 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer & rugby but not volleyball? 6 6 4 X 7 6 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer or rugby? 6 6 4 7 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer or rugby? 6 6 6 6 4 4 7 7 5 5 6 6 1 1 57 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer or rugby? + 6 6 6 6 + 4 4 34 + + 7 7 5 5 + 6 6 1 1 57 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer or rugby but not volleyball?

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer or rugby but not volleyball? 6 6 4 7 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer or rugby but not volleyball? 6 6 4 X X 7 5 X 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer or rugby but not volleyball? + 6 6 + 4 X X 7 5 X 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had soccer or rugby but not volleyball? + 6 6 + 4 X 7 16 X 5 X 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had exactly 2 teams? 6 6 4 7 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 92 cities were surveyed to determine sports teams. 24 had soccer had soccer & rugby had all three 23 had rugby had soccer & volleyball 19 had volleyball had rugby & volleyball How many had exactly 2 teams? 6 6 + 4 + 7 17 5 6 1 57

A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only?

A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region.

A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8

A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8 We are told that 98 had none of the 3.

A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8 We are told that 98 had none of the 3. 98

A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? ? + Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 + Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 Begin with the innermost region. 8 We are told that 98 had none of the 3. Continue with the other interior regions. 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 At this point, is might be useful to look at what we are actually asked to find. 8 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 At this point, is might be useful to look at what we are actually asked to find. 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 99 = 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 99 = 8 So, even though we don’t know the 2 individual numbers in the green boxes, ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 99 = 8 So, even though we don’t know the 2 individual numbers in the green boxes, we do know now that there are 65 in that combined region. ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We don’t have enough info to decide what goes here and here… but we do know that the numbers in the ‘Dog’ circle must sum to 99. A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 65 99 = 8 So, even though we don’t know the 2 individual numbers in the green boxes, we do know now that there are 65 in that combined region. ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 65 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We also don’t have enough info to decide what goes In the two other subregions in the ‘Cat’ circle but we do know that the sum in that circle must be 76. A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 65 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We also don’t have enough info to decide what goes In the two other subregions in the ‘Cat’ circle but we do know that the sum in that circle must be 76. A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 65 76 = 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We also don’t have enough info to decide what goes In the two other subregions in the ‘Cat’ circle but we do know that the sum in that circle must be 76. A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 65 76 = 8 Using the same logic as before, we know that there are 42 in that combined region. ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises We also don’t have enough info to decide what goes In the two other subregions in the ‘Cat’ circle but we do know that the sum in that circle must be 76. A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 We also know that 65 42 76 = 8 Using the same logic as before, we know that there are 42 in that combined region. ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 65 42 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 ? 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 ? ? = 260 98

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 ? ? = 260 98 239 + ? = 260

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 ? ? = 260 98 239 + ? = 260 ? = 21

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 The final piece of information that we know is that there were 260 families surveyed. 65 42 8 21 ? = 260 98 239 + ? = 260 ? = 21

None of the remaining information directly tells us about the other interior regions. But, we still must use what we are left with. MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat had a dog, a cat & a parakeet How many had a parakeet only? 26 21 65 42 8 21 98

Shade the Venn diagram to represent the set A' U (A ∩ B)

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Shade the Venn diagram to represent the set A' U (A ∩ B)

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Presentation on theme: "Shade the Venn diagram to represent the set A' U (A ∩ B)"— Presentation transcript:

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