1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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(B') = 41 B A U C

8. 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(B') = 41 B
Answer:
w = z = 9
r = n = 23
x = p = 10
y = m = 21 A U C

9. 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 ∩ C) = 11 B A U C

10. 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 ∩ C) = 11 B
Answer:
n(A) = 12
n(B) = 3
n(C) = 18 A U C

11. 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

12. 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

13. 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 U A C B
Fill in the number of elements in each region.
Answer: see next slide

14. 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 U A C B
How many had only volleyball? 6 6 4 7 5 6 1 57

15. 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 U A C B
How many had only volleyball? 6 6 4 1 7 5 6 1 57

16. 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 U A C B
How many had soccer & rugby but not volleyball? 6 6 4 7 5 6 1 57

17. 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 U A C B
How many had soccer & rugby but not volleyball? 6 6 4 7 6 5 6 1 57

18. 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 U A C B
How many had soccer or rugby? 6 6 4 7 5 6 1 57

19. 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 U A C B
How many had soccer or rugby? 6 6 4 34 7 5 6 1 57

20. 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 U A C B
How many had soccer or rugby but not volleyball? 6 6 4 7 5 6 1 57

21. 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 U A C B
How many had soccer or rugby but not volleyball? 6 6 4 7 16 5 6 1 57

22. 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 U A C B
How many had exactly 2 teams? 6 6 4 7 5 6 1 57

23. 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 U A C B
How many had exactly 2 teams? 6 6 4 17 7 5 6 1 57

24. 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 U A C B
How many had a parakeet only?

25. 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 U A C B
How many had a parakeet only? 21