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) B A U

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) B A U

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? U W X 𝑟 3 𝑟 2 𝑟 4 𝑟 6 𝑟 5 𝑟 7 𝑟 1 𝑟 8 Y

What regions make up X ∩ W' ∩ Y ? MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises What regions make up X ∩ W' ∩ Y ? U W X 𝑟 3 𝑟 2 𝑟 4 𝐴𝑛𝑠𝑤𝑒𝑟: 𝑟 7 𝑟 6 𝑟 5 𝑟 7 𝑟 1 𝑟 8 Y

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 B A U

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 B A Answer: y = 13 x = 3 z = 8 w = 30 U

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) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(B') = 41 B A U C

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) = 2 n(C) = 29 n(A ∩ C) = 10 n(A ∩ C') = 28 n(A' ∩ B' ∩ C') = 8 n(A ∩ B) = 9 n(B ∩ C) = 11 n(B') = 41 B Answer: w = 2 z = 9 r = 8 n = 23 x = 7 p = 10 y = 8 m = 21 A 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) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ∩ C) = 11 B A 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) = 3 n(A ─ C) = 1 n(U) = 19 n(A ∩ C) = 11 n(C ─ A) = 7 n(B ∩ C) = 11 B Answer: n(A) = 12 n(B) = 3 n(C) = 18 A U C

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 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

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises 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 Answer: n(A ∪ D) = 285 n(B ⋂ F) = 9

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B Fill in the number of elements in each region. Answer: see next slide

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had only volleyball? 6 6 4 7 5 6 1 57

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had only volleyball? 6 6 4 1 7 5 6 1 57

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had soccer & rugby but not volleyball? 6 6 4 7 5 6 1 57

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had soccer & rugby but not volleyball? 6 6 4 7 6 5 6 1 57

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had soccer or rugby? 6 6 4 7 5 6 1 57

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had soccer or rugby? 6 6 4 34 7 5 6 1 57

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had soccer or rugby but not volleyball? 6 6 4 7 5 6 1 57

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had soccer or rugby but not volleyball? 6 6 4 7 16 5 6 1 57

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had exactly 2 teams? 6 6 4 7 5 6 1 57

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 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball 19 had volleyball 13 had rugby & volleyball U A C B How many had exactly 2 teams? 6 6 4 17 7 5 6 1 57

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet U A C B How many had a parakeet only?

MATH 110 Sec 2-4: More Venn Diagrams Practice Exercises A survey of 260 families: 99 had a dog 98 had neither a dog nor a cat 76 had a cat and also had no parakeet 34 had a dog & cat 8 had a dog, a cat & a parakeet U A C B How many had a parakeet only? 21