Deck 8: Sets and Probability

Question 1

Tell whether the statement is true or false.

- $8 \in\{16,24,32,40,48\}$

Answer 1

False

Question 2

Tell whether the statement is true or false.

- $\{4,8,13\}=\{0,4,8,13\}$

Answer 2

False

Question 3

Tell whether the statement is true or false.

- $\{x \mid x$ is an even counting number between 8 and 14 $\}=\{6\}$

Answer 3

False

Question 4

Tell whether the statement is true or false.

- $\{57,58,57,58\}=\{57,58\}$

Question 5

Tell whether the statement is true or false.

- $\{2,12,26,7,32\}=\{32,12,7,62,2\}$

Question 6

Tell whether the statement is true or false.

- $13 \notin\{x \mid x$ is an even counting number $\}$

Question 7

Tell whether the statement is true or false.

- $\{x \mid x$ is a counting number greater than 34 $\}=\{34,35,36, \ldots\}$

Question 8

Insert " $\subseteq$ " or "q" in the blank to make the statement true.

- $\{4,6,8\} \_\{3,4,5,6,8\}$

A) $\nsubseteq$
B) $\subseteq$

Question 9

Insert " $\subseteq$ " or "q" in the blank to make the statement true.

- $\{7,21,26\} \_\{16,21,26,36\}$

A) $\subseteq$
B) $\Phi$

Question 10

Insert " $\subseteq$ " or "q" in the blank to make the statement true.

- $\{b, c, h, f\}-\{b, c, h, f, k\}$

A) $\subseteq$
B) $\nsubseteq$

Question 11

Insert " $\subseteq$ " or "q" in the blank to make the statement true.

- $\{1,3,5\} \_\{x \mid x \text { is an odd counting number }\}$

A) $\Phi$
B) $\subseteq$

Question 12

Insert " $\subseteq$ " or "q" in the blank to make the statement true.

-{k, b, d} _{k, b, d}

A) $\nsubseteq$
B) $\subseteq$

Question 13

Insert " $\subseteq$ " or "q" in the blank to make the statement true.

- $\{x \mid x$ is a counting number larger than 5 $\} \_\{7,8,9, \ldots\}$

A) $\nsubseteq$
B) $\subseteq$

Question 14

Find the number of subsets of the set.

-{8, 9, 10}

A) 7
B) 3
C) 6
D) 8

Question 15

Find the number of subsets of the set.

- $\{0\}$

A) 1
B) 4
C) 0
D) 2

Question 16

Find the number of subsets of the set.

- $\{x \mid x$ is a day of the week $\}$

A) 128
B) 256
C) 124
D) 127

Question 17

Find the number of subsets of the set.

- $\{x \mid x$ is an even number between 15 and 35 $\}$

A) 1024
B) 32
C) 34
D) 5

Question 18

Find the number of subsets of the set.

- $\{1,2,3, \ldots, 9\}$

A) 508
B) 16
C) 1024
D) 512

Question 19

Find the complement of the set.

- $\{x \mid x$ is an integer strictly between 0 and 9 $\}$ if $U$ is the set of all integers

A) $\{x x$ is an integer $\geq 9\}$
B) $\{x \mid x$ is an integer $\geq 0$ or $\leq 9\}$
C) $\{x \mid x$ is an integer $\geq 0\}$
D) $\{x \mid x$ is an integer $\leq 0$ or $\geq 9\}$

Question 20

Find the complement of the set.

- $\{x \mid x$ is a whole number less than 6 $\}$ if $U$ is the set of all whole numbers

A) $\{x \mid x$ is a whole number $\geq 6\}$
B) $\{x \mid x$ is a whole number $>6\}$
C) $\{x \mid x$ is a whole number $<6\}$
D) $\{x \mid x$ is a whole number $\leq 6\}$

Question 21

Decide whether the statement is true or false.

- $\{4,8,12,16\} \cap\{4,12\}=\{4,8,12,16\}$

Question 22

Decide whether the statement is true or false.

- $\{0\} \cap \varnothing=\{0\}$

Question 23

Decide whether the statement is true or false.

- $\{7,14,21,28\} \cup\{7,21\}=\{7,14,21,28\}$

Question 24

Decide whether the statement is true or false.

- $\{2,13,12\} \cup\{12,2,13\}=\{2,12\}$

Question 25

Decide whether the statement is true or false.

- $\{8,14,15\} \cup \varnothing=\{8,14,15\}$

Question 26

Decide whether the statement is true or false.

- $\{15,14,7\} \cap \varnothing=\{15,14,7\}$

Question 27

Decide whether the statement is true or false.

- $\{3,5,7\} \cap\{4,6,8\}=\{3,5,7,4,6,8\}$

Question 28

Decide whether the statement is true or false.

- $\{8,5,9\} \cup\{8,5,9\}=\varnothing$

Question 29

Decide whether the statement is true or false.

- $\varnothing \cap \varnothing=\varnothing$

Question 30

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

- $\mathrm{A}^{\prime}$

A) $\{q, s, u, w, y\}$
B) $\{\mathrm{r}, \mathrm{t}, \mathrm{v}, \mathrm{x}, \mathrm{z}\}$
C) $\{q, s, v, w, x, y, z\}$
D) $\{\mathrm{r}, \mathrm{t}, \mathrm{z}\}$

Question 31

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

-B'

A) $\{q, s, u, v, w, x, y, z\}$
B) $\{q, s, y, z\}$
C) $\{r, t, u, v, w, x\}$
D) $\{q, r, s, t, u\}$

Question 32

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

- $A \cap B^{\prime}$

A) $\{q, s, t, u, v, w, x, y\}$
B) $\{r, s, t, u, v, w, x, z\}$
C) $\{t, v, x\}$
D) $\{\mathrm{u}, \mathrm{w}\}$

Question 33

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

- $(A \cup B)^{\prime}$

A) $\{\mathrm{s}, \mathrm{u}, \mathrm{w}\}$
B) $\{t, v, x\}$
C) $\{\mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{z}\}$
D) $\{r, t, v, x\}$

Question 34

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

- $(A \cap B)^{\prime}$

A) $\{q, s, t, u, v, w, x, y\}$
B) $\{s, u, w\}$
C) $\{t, v, x\}$
D) $\{r, t, u, v, w, x, z\}$

Question 35

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

- $\mathrm{A}^{\prime} \cup \mathrm{B}$

A) $\{s, u, w\}$
B) $\{q, r, s, t, v, x, y, z\}$
C) $\{q, s, t, u, v, w, x, y\}$
D) $\{\mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{z}\}$

Question 36

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

- $\mathrm{A} \cup(\mathrm{B} \cap \mathrm{C})$

A) $\{q, y, z\}$
B) $\{q, w, y\}$
C) $\{q, r, w, y, z\}$
D) $\{q, s, u, w, y, z\}$

Question 37

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

- $B \cap(A \cup C)$

A) $\{q, w, y\}$
B) $\{q, s, u, w, y, z\}$
C) $\{q, s, y, z\}$
D) $\{q, r, w, y, z\}$

Question 38

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

- $\mathrm{C}^{\prime} \cup \mathrm{A}^{\prime}$

A) $\{q, r, s, t, u, v, x, z\}$
B) $\{s, t\}$
C) $\{q, s, u, v, w, x, y, z\}$
D) $\{w, y\}$

Question 39

Let $U=\{q, r, s, t, u, v, w, x, y, z\} ; A=\{q, s, u, w, y\} ; B=\{q, s, y, z\} ;$ and $C=\{v, w, x, y, z\}$ . List the members of the indicated set, using set braces.

- $\mathrm{C}^{\prime} \cap \mathrm{A}^{\prime}$

A) $\{\mathrm{r}, \mathrm{t}\}$
B) $\{q, s, u, v, w, x, y, z\}$
C) $\{w, y\}$
D) $\{q, r, s, t, u, v, x, z\}$

Question 40

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

- $A \cap K$

A) $\{c, p, r, t\}$
B) $\{c, h, p, r, s, t, w\}$
C) $\{h, s, w\}$
D) $\{\mathrm{c}, \mathrm{h}, \mathrm{s}, \mathrm{t}, \mathrm{w}\}$

Question 41

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

- $\mathrm{L} \cap \mathrm{K}$

A) $\{\mathrm{c}, \mathrm{n}, \mathrm{r}, \mathrm{s}, \mathrm{t}\}$
B) $\{c, h, n, w\}$
C) $\{\mathrm{r}, \mathrm{s}, \mathrm{t}\}$
D) $\{c, h, n, r, s, t, w\}$

Question 42

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

- $\mathrm{K}^{\prime} \cap \mathrm{L}$

A) $\{\mathrm{h}, \mathrm{w}\}$
B) $\{r, s, t\}$
C) $\{c, n\}$
D) $\{\mathrm{c}, \mathrm{n}, \mathrm{p}\}$

Question 43

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

-L' $\cap$ A

A) $\{c, s\}$
B) $\{\mathrm{h}, \mathrm{n}, \mathrm{t}, \mathrm{w}\}$
C) $\{n, r, t\}$
D) $\{\mathrm{h}, \mathrm{p}, \mathrm{w}\}$

Question 44

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

- $\mathrm{A} \cap \mathrm{K} \cap \mathrm{L}$

A) $\{s\}$
B) $\{c, h, n, p, r, s, t, w\}$
C) $\{n, p, s\}$
D) $\{n, p\}$

Question 45

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

- $A \cup L$

A) $\{h, n, p, r, t, w\}$
B) $\{c, s\}$
C) $\{\mathrm{c}, \mathrm{h}, \mathrm{n}, \mathrm{p}, \mathrm{r}, \mathrm{s}, \mathrm{t}, \mathrm{w}\}$
D) $\{c, n, p\}$

Question 46

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

- $\mathrm{K} \cup \mathrm{L}$

A) $\{c, h, n, r, s, t, w\}$
B) $\{r, s, t\}$
C) $\{\mathrm{c}, \mathrm{h}, \mathrm{n}, \mathrm{w}\}$
D) $\{n, r, t\}$

Question 47

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

- $\mathrm{A}^{\prime} \cup \mathrm{L}$

A) $\{h, n, p, r, t, w\}$
B) $\{c, n, r, s, t\}$
C) $\{\mathrm{h}, \mathrm{p}, \mathrm{w}\}$
D) $\{\mathrm{n}, \mathrm{r}, \mathrm{t}\}$

Question 48

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

- $\mathrm{L}^{\prime} \cup \mathrm{K}^{\prime}$

A) $\{\mathrm{c}, \mathrm{h}, \mathrm{p}, \mathrm{s}, \mathrm{w}\}$
B) $\{r, s, t\}$
C) $\{\mathrm{c}, \mathrm{h}, \mathrm{n}, \mathrm{p}, \mathrm{w}\}$
D) $\{p\}$

Question 49

Let $\mathrm{U}$ be the smallest possible universal set that includes all of the crops listed; and let $\mathrm{A}, \mathrm{K}$ , and $\mathrm{L}$ be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find the indicated set.

- $\mathrm{A}^{\prime} \cap \mathrm{K}^{\prime}$

A) $\{n\}$
B) $\{\mathrm{c}, \mathrm{p}, \mathrm{r}, \mathrm{t}\}$
C) $\{\mathrm{c}, \mathrm{n}, \mathrm{p}, \mathrm{r}, \mathrm{t}\}$
D) $\varnothing$

Question 50

Shade the Venn diagram to represent the set.

- $\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}$

A)
B)

Question 51

Shade the Venn diagram to represent the set.

- $\mathrm{A}^{\prime} \cup \mathrm{B}^{\prime}$

A)
B)

Question 52

Shade the Venn diagram to represent the set.

- $(A \cup B) \cap(A \cap B)^{\prime}$

A)
B)

Question 53

Shade the Venn diagram to represent the set.

- $(A \cap B) \cup(A \cup B)^{\prime}$

A)
B)

Question 54

Shade the Venn diagram to represent the set.

- $\left(A \cap B \cap C^{\prime}\right)^{\prime}$

A)
B)

Question 55

Shade the Venn diagram to represent the set.

- $\left(A \cup B \cup C^{\prime}\right)^{\prime}$

A)

B)

Question 56

Shade the Venn diagram to represent the set.

- $C^{\prime} \cap(A \cup B)$

A)
B)

Question 57

Shade the Venn diagram to represent the set.

- $\left(A^{\prime} \cup B\right) \cap C$

A)
B)

Question 58

Shade the Venn diagram to represent the set.

- $\mathrm{A} \cup\left(\mathrm{B} \cap \mathrm{C}^{\prime}\right)$

A)
B)

Question 59

Shade the Venn diagram to represent the set.

- $\mathrm{B} \cup\left(\mathrm{A} \cap \mathrm{C}^{\prime}\right)$

A)
B)

Question 60

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.

- $n(U)=60, n(A)=29, n(B)=17$ , and $n(A \cap B)=3$ . Find $n(A \cup B)^{\prime}$ .

A) 43
B) 14
C) 46
D) 17

Question 61

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.

- $\mathrm{n}(\mathrm{U})=235, \mathrm{n}(\mathrm{A})=80, \mathrm{n}(\mathrm{B})=100, \mathrm{n}(\mathrm{A} \cap \mathrm{B}) \quad=35, \mathrm{n}(\mathrm{A} \cap \mathrm{C})=38, \mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=18$ , $n\left(A^{\prime} \cap B \cap C^{\prime}\right)=47$ , and $n\left(A^{\prime} \cap B^{\prime} \cap C^{\prime}\right)=60$ . Find $n(C)$ .

A) 50
B) 46
C) 86
D) 30

Question 62

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.

- $\mathrm{n}(\mathrm{A})=85, \mathrm{n}(\mathrm{B})=93, \mathrm{n}(\mathrm{C})=87, \mathrm{n}(\mathrm{A} \cap \mathrm{B})=17, \mathrm{n}(\mathrm{A} \cap \mathrm{C})=19, \mathrm{n}(\mathrm{B} \cap \mathrm{C})=13, \mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=11$ , and $\mathrm{n}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime} \cap \mathrm{C}^{\prime}\right)=171$ . Find $\mathrm{n}(\mathrm{U})$

A) 227
B) 398
C) 408
D) 312

Question 63

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.

- $\mathrm{n}(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C})=157, \mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=21, \mathrm{n}(\mathrm{A} \cap \mathrm{B})=44, \mathrm{n}(\mathrm{A} \cap \mathrm{C})=41, \mathrm{n}(\mathrm{B} \cap \mathrm{C})=39, \mathrm{n}(\mathrm{A})=106$ , $n(B)=78$ , and $n(C)=76$ . Find $n\left(A^{\prime} \cap B \cap C\right)$

A) 20
B) 19
C) 17
D) 18

Question 64

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.

- $n(U)=114, n(A)=44, n(B)=39, n(C)=48, n(A \cap B)=5, n(A \cap C)=8, n(B \cap C)=8$ , and $n(A \cap(B \cap C))=4$ . Find $n\left(A \cap(B \cup C)^{\prime}\right)$ .

A) 35
B) 4
C) 38
D) 3

Question 65

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.

- $n(U)=118, n(A)=37, n(B)=50, n(C)=43, n(A \cap B)=8, n(A \cap C)=6, n(B \cap C)=7$ , and $n(A \cap(B \cap C))=5$ . Find $n\left(((A \cup B) \cup C)^{\prime}\right)$ .

A) 5
B) 32
C) 4
D) 28

Question 66

Use a Venn Diagram and the given information to determine the number of elements in the indicated set.

- $n(U)=87, n(A)=23, n(B)=30, n(C)=53, n(A \cap B)=6, n(A \cap C)=9, n(B \cap C)=8$ , and $\mathrm{n}(\mathrm{A} \cap(\mathrm{B} \cap \mathrm{C}))=4$ . Find $\mathrm{n}(\mathrm{A} \cap(\mathrm{B} \cap \mathrm{C}))$ .

A) 3
B) 4
C) 12
D) 15

Question 67

Use a Venn diagram to decide if the statement is true or false.

- $A \cap B^{\prime}=\left(A^{\prime} \cup B\right)^{\prime}$

Question 68

Use a Venn diagram to decide if the statement is true or false.

- $\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)^{\prime}=\mathrm{A} \cap \mathrm{B}^{\prime}$

Question 69

Use a Venn diagram to decide if the statement is true or false.

- $\left(\mathrm{A} \cup \mathrm{B}^{\prime}\right)^{\prime}=\mathrm{A}^{\prime} \cap \mathrm{B}$

Question 70

Use a Venn diagram to decide if the statement is true or false.

- $\left(\mathrm{A}^{\prime} \cup \mathrm{B}\right)^{\prime}=\mathrm{A}^{\prime} \cap \mathrm{B}$

Question 71

Use a Venn diagram to decide if the statement is true or false.

- $(A \cap B) \cup C=(A \cup C) \cap(A \cup B)$

Question 72

Use a Venn diagram to decide if the statement is true or false.

- $\mathrm{B} \cup(\mathrm{A} \cap \mathrm{C})=(\mathrm{A} \cup \mathrm{B}) \cap(\mathrm{B} \cup \mathrm{C})$

Question 73

Use a Venn diagram to decide if the statement is true or false.

- $A^{\prime} \cup(B \cap C)=\left(A^{\prime} \cup B\right) \cap\left(A^{\prime} \cup C\right)$

Question 74

Use a Venn diagram to decide if the statement is true or false.

- $\mathrm{A} \cup(\mathrm{B} \cap \mathrm{C})^{\prime}=\left(\mathrm{A} \cup \mathrm{B}^{\prime}\right) \cap\left(\mathrm{A} \cup \mathrm{C}^{\prime}\right)$

Question 75

Use a Venn diagram to decide if the statement is true or false.

- $A \cup(B \cup C)^{\prime}=\left(A \cup B^{\prime}\right) \cap\left(A \cup C^{\prime}\right)$

Question 76

Use a Venn diagram to decide if the statement is true or false.

-(A ? B) ? (A ? C) = A ? (B ? C)

Question 77

Use a Venn diagram to answer the question.

-At East Zone University (EZU) there are 683 students taking College Algebra or Calculus. 281 are taking College Algebra, 456 are taking Calculus, and 54 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus?

A)6 29
B) 227
C) 173
D) 402

Question 78

Use a Venn diagram to answer the question.

-At East Zone University (EZU) there are 688 students taking College Algebra or Calculus. 495 are taking College Algebra, 210 are taking Calculus, and 17 are taking both College Algebra and Calculus. How many are taking Calculus but not Algebra?

A) 671
B) 461
C) 478
D) 193

Question 79

Use a Venn diagram to answer the question.

-A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 900 responses with the following results:
270 were interested in an interview show and a documentary, but not reruns;
36 were interested in an interview show and reruns, but not a documentary;
126 were interested in reruns but not an interview show;
216 were interested in an interview show but not a documentary;
90 were interested in a documentary and reruns;
54 were interested in an interview show and reruns;
72 were interested in none of the three.
How many are interested in exactly one kind of show?

A) 422
B) 432
C) 412
D) 442

Question 80

Use a Venn diagram to answer the question.

-A survey of 180 families showed that
67 had a dog;
52 had a cat;
22 had a dog and a cat;
70 had neither a cat nor a dog, and in addition did not have a parakeet;
4 had a cat, a dog, and a parakeet.
How many had a parakeet only?

A) 28
B) 18
C) 23
D) 13