Deck 7: Logic, Sets, and Counting

Question 1

Construct a truth table for the proposition:

-~p $\Lambda$ ~q

A)
B)
C)
D)

Answer 1

Question 2

Construct a truth table for the proposition:

-p (p $\Lambda$ ~p)

A)
B)
C)
D)

Answer 2

Question 3

Construct a truth table for the proposition:

-p $\rightarrow$ ~q

A)
B)
C)
D)

Answer 3

Question 4

Construct a truth table for the proposition:

-~p $\rightarrow$ (~p $\Lambda$ s)

A)
B)
C)
D)

Question 5

Construct a truth table for the proposition and determine whether it is a contingency, a tautology, or a contradiction: ~p ∨ q.

Question 6

Construct a truth table for the proposition and determine whether it is a contingency, a tautology, or a contradiction: (q ∨ p) ∧ ~q.

Question 7

Construct a truth table to determine whether or not the following implication is true:

Question 8

Construct a truth table to decide if the two statements are equivalent:

-~p ~q; ~(p $\Lambda$ q)

Question 9

Construct a truth table to decide if the two statements are equivalent:

-~p $\Lambda$ ~q; ~(p q)

Question 10

Construct a truth table to decide if the two statements are equivalent:

-

Question 11

Construct a truth table to decide if the two statements are equivalent:

-

Question 12

Construct a truth table to decide if the two statements are equivalent:

-~(~q); q

Question 13

Tell whether the statement is true or false:

-3 $\in$ {6, 9, 12, 15, 18}

Question 14

Tell whether the statement is true or false:

-7 $\notin$ 0 {14, 21, 28, 35, 42}

Question 15

Tell whether the statement is true or false:

-0 $\notin$ $\phi$

Question 16

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; andU= {1,2,3,4,5,6,7,8} Determine whether the given statement is true or false.

-C $\subseteq$ D

Question 17

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; andU= {1,2,3,4,5,6,7,8} Determine whether the given statement is true or false.

-U $\subseteq$ A

Question 18

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; andU= {1,2,3,4,5,6,7,8} Determine whether the given statement is true or false.

-{5} $\subseteq$ D

Question 19

Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; andU= {1,2,3,4,5,6,7,8} Determine whether the given statement is true or false.

-A $\subset$ A

Question 20

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false

-{9} $\subset$ A

Question 21

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false

-{3, 0, 8} $\in$ A

Question 22

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false

-{9} $\subset$ A

Question 23

Let A = {6, 4, 1, {3, 0, 8}, {9}}. Determine whether the statement is true or false

-{3, 0, 8} $\in$ A

Question 24

One of the following is false; indicate by letter which one:

A) 4 $\in$ {3, 4, 5, 6}
B) 4 $\subset$ {3, 4, 5, 6}
C) 5 $\in$ {3, 4, 5, 6}
D) {4} $\subset$ {3, 4, 5, 6}

Question 25

Use the Venn diagram to find the requested set:

-Find A.

A) { 7, 2, 6, z}
B) { 6}
C) { 6, z, q, h}
D) { 7, 2, 6}

Question 26

Use the Venn diagram to find the requested set:

-Find A $\cap$ B.

A) { m}
B) { e, c, i, g, m, q, t}
C) { e, c, i, g, q, t}
D) { c, i}

Question 27

Use the Venn diagram to find the requested set:

-Find A $\cup$ B.

A) { b, j}
B) { q}
C) { e, b, j, h, q, m, t}
D) { e, b, j, h, m, t}

Question 28

Use the Venn diagram to find the requested set:

-Find A' $\cap$ B'.

A) $\phi$
B) { 7, 3, 4, z, r, h}
C) { 7}
D) { 4}

Question 29

Use a Venn Diagram and the given information to determine the number of elements in the indicated region:

-

A) 60
B) 64
C) 52
D)51

Question 30

Use a Venn Diagram and the given information to determine the number of elements in the indicated region:

-

A) 42
B) 13
C)36
D)49

Question 31

Use a Venn Diagram and the given information to determine the number of elements in the indicated region:
-

Question 32

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let
A = {n ? N| n > 50}
B = {n ? N| n < 250}
O = {n ? N| n is odd}
E = {n ? N| n is even}

-A'

A) infinite
B) finite

Question 33

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let
A = {n ∈ N| n > 50}
B = {n ∈ N| n < 250}
O = {n ∈ N| n is odd}
E = {n ∈ N| n is even}

-B $\cup$ E

A) finite
B) infinite

Question 34

Use the Venn diagram below to find the number of elements in the region.


-

A) 29
B) 39
C) 14
D) 24

Question 35

Use the Venn diagram below to find the number of elements in the region.


-n(A $\cap$ C)

A) 18
B) 2
C) 37
D)10

Question 36

Use the Venn diagram below to find the number of elements in the region.


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

A) 14
B) 33
C)11
D)15

Question 37

Use the addition principle for counting to solve the problem:

-If n(A) = 5, n(B) = 11 and n(A $\cap$ B) = 3, what is n(A $\cup$ B)?

A) 11
B) 14
C)13
D)12

Question 38

Use the addition principle for counting to solve the problem:

-If n(A) = 40, n(B) = 117 and n(A $\cup$ B) = 137, what is n(A $\cap$ B)?

A) 20
B) 10
C)40
D)22

Question 39

Use the addition principle for counting to solve the problem:

-If n(B) = 24, n(A $\cap$ B) =5, and n(A $\cup$ B) = 42, find n(A).

A) 23
B) 24
C)25
D)21

Question 40

Use the addition principle for counting to solve the problem:

-If n(A) = 20, n(A $\cup$ B) = 58, and n(A $\cap$ B) = 16, find n(B).

A) 58
B) 54
C)55
D)53

Question 41

Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many of the students surveyed own no dogs?

A) 15
B) 8
C) 20
D) 3

Question 42

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 300 responses with the following results:
90 were interested in an interview show and a documentary, but not reruns.
12 were interested in an interview show and reruns but not a documentary
42 were interested in reruns but not an interview show.
72 were interested in an interview show but not a documentary.
30 were interested in a documentary and reruns.
18 were interested in an interview show and reruns.
24 were interested in none of the three.
How many are interested in exactly one kind of show?

A) 154
B) 144
C) 134
D) 124

Question 43

License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed?

A) 308,915,776
B) 1,757,600
C) 175,760
D) 1,000,000
E)17,576,000

Question 44

Evaluate:

-4!

A) 48
B) 24
C) 12
D) 6

Question 45

Evaluate:

-

A) 32
B) 15
C) 16
D) 8

Question 46

Evaluate:

-

A) 42
B) 2!
C) 7
D)

Question 47

Evaluate:

-

A) 1
B) 72
C) 9
D) 36

Question 48

Evaluate:

-

A) 90
B) 19
C) 45
D) 8

Question 49

Evaluate:

-

A) 2
B) 24
C) 360
D) 30

Question 50

Evaluate:

-

A) 28
B) 4
C) 1440
D) 720

Question 51

Evaluate:

-

A) 720
B) 6
C) 1
D) 7