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

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U

A B

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

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U

A B

What regions make up X ∩ W' ∩ Y ?

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U W X

Y𝑟1

𝑟6𝑟5 𝑟7𝑟8

𝑟 4𝑟3𝑟2

What regions make up X ∩ W' ∩ Y ?

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U W X

Y𝑟1

𝑟6𝑟5 𝑟7𝑟8

𝑟 4𝑟3𝑟2

𝐴𝑛𝑠𝑤𝑒𝑟 :𝑟7

Use the given information to fill in the number of elements for each region in the Venn diagram below.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U

A B

n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38

Use the given information to fill in the number of elements for each region in the Venn diagram below.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U

A BAnswer:y = 13x = 3 z = 8 w = 30

n(A) = 16, n(B) = 21, n(A ∩ B) = 13, n(A') = 38

Find the number of elements in each region below.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U

A B

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

C

Find the number of elements in each region below.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U

A B

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

C

Answer:w = 2 z = 9r = 8 n = 23x = 7 p = 10y = 8 m = 21

Find the number of elements in sets A, B & C if:

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U

A B

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

C

Find the number of elements in sets A, B & C if:

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

U

A B

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

C

Answer:n(A) = 12n(B) = 3 n(C) = 18

MATH 110 Sec 2-4: More Venn DiagramsPractice 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, findn(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

Total 152 66 55 133 406

MATH 110 Sec 2-4: More Venn DiagramsPractice 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, findn(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

Total 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 DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BFill 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 DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had only volleyball?

7

6 4

65

6

1 57

92 cities were surveyed to determine sports teams.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had only volleyball?

7

6 4

65

6

1 57

1

92 cities were surveyed to determine sports teams.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had soccer & rugby but not volleyball?

7

6 4

65

6

1 57

92 cities were surveyed to determine sports teams.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had soccer & rugby but not volleyball?

7

6 4

65

6

1 57

6

92 cities were surveyed to determine sports teams.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had soccer or rugby?

7

6 4

65

6

1 57

92 cities were surveyed to determine sports teams.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had soccer or rugby?

7

6 4

65

6

1 57

34

92 cities were surveyed to determine sports teams.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had soccer or rugby but not volleyball?

7

6 4

65

6

1 57

92 cities were surveyed to determine sports teams.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had soccer or rugby but not volleyball?

7

6 4

65

6

1 57

16

92 cities were surveyed to determine sports teams.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had exactly 2 teams?

7

6 4

65

6

1 57

92 cities were surveyed to determine sports teams.

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

24 had soccer 13 had soccer & rugby 7 had all three 23 had rugby 12 had soccer & volleyball19 had volleyball 13 had rugby & volleyball

U

A

C

BHow many had exactly 2 teams?

7

6 4

65

6

1 57

17

A survey of 260 families:

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

99 had a dog 98 had neither a dog nor a cat76 had a cat and also had no parakeet34 had a dog & cat 8 had a dog, a cat & a parakeet

U

A

C

BHow many had a parakeet only?

A survey of 260 families:

MATH 110 Sec 2-4: More Venn DiagramsPractice Exercises

99 had a dog 98 had neither a dog nor a cat76 had a cat and also had no parakeet34 had a dog & cat 8 had a dog, a cat & a parakeet

U

A

C

BHow many had a parakeet only?

21