Question 1

Construct a truth table for the proposition:
-p $\rightarrow$ ~q

Accepted Answer

A)   
B)   
C)   
D)     C

Question 2

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).

Accepted Answer

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

Question 3

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)?

Accepted Answer

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

Question 4

Tell whether the statement is true or false:
-7 $ \notin $0 {14, 21, 28, 35, 42}

Accepted Answer

A) True 
 B)False

Question 5

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)?

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Construct a truth table for the proposition:
-~p $ \Lambda $~q

Accepted Answer

A)   
B)   
C)   
D)

Question 8

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

Accepted Answer

The answer of Use a Venn Diagram and the given...

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

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?

Accepted Answer

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

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

Construct a truth table to decide if the two statements are equivalent:
-~p $ \Lambda $ ~q; ~(p q)

Accepted Answer

A) True 
 B)False

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

Evaluate:
-

Accepted Answer

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

Question 15

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'

Accepted Answer

A)   infinite
B)   finite

Question 16

Evaluate:
-

Accepted Answer

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

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

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

The answer of Construct a truth table for the proposition...

Question 19

Evaluate:
-4!

Accepted Answer

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

Question 20

Use the Venn diagram below to find the number of elements in the region.
 
-n(A $\cap$ C)

Accepted Answer

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

Exam 7: Logic, Sets, and Counting

Construct a truth table for the proposition: -p $\rightarrow$ ~q

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) .

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) ?

Tell whether the statement is true or false: -7 $\notin$ 0 {14, 21, 28, 35, 42}

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) ?

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

Construct a truth table for the proposition: -~p $\Lambda$ ~q

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

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

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?

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

Construct a truth table to decide if the two statements are equivalent: -~p $\Lambda$ ~q; ~(p $Construct a truth table to decide if the two statements are equivalent: -~p \Lambda ~q; ~(p q)$ q)

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

Evaluate: -

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'

Evaluate: -

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

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

Evaluate: -4!

Use the Venn diagram below to find the number of elements in the region. $Use the Venn diagram below to find the number of elements in the region. -n(A \cap C) A) 18 B) 2 C) 37 D) 10$ -n(A $\cap$ C)

Exam 7: Logic, Sets, and Counting

Construct a truth table for the proposition: -p →\rightarrow→ ~q

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) .

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) ?

Tell whether the statement is true or false: -7 ∉ \notin ∈/ 0 {14, 21, 28, 35, 42}

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) ?

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

Construct a truth table for the proposition: -~p Λ \Lambda Λ ~q

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

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

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?

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

Construct a truth table to decide if the two statements are equivalent: -~p Λ \Lambda Λ ~q; ~(p q)

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

Evaluate: -

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'

Evaluate: -

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

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

Evaluate: -4!

Use the Venn diagram below to find the number of elements in the region. -n(A ∩\cap∩ C)

Construct a truth table for the proposition: -p $\rightarrow$ ~q

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) .

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) ?

Tell whether the statement is true or false: -7 $\notin$ 0 {14, 21, 28, 35, 42}

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) ?

Construct a truth table for the proposition: -~p $\Lambda$ ~q

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

Construct a truth table to decide if the two statements are equivalent: -~p $\Lambda$ ~q; ~(p $Construct a truth table to decide if the two statements are equivalent: -~p \Lambda ~q; ~(p q)$ q)

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

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

Use the Venn diagram below to find the number of elements in the region. $Use the Venn diagram below to find the number of elements in the region. -n(A \cap C) A) 18 B) 2 C) 37 D) 10$ -n(A $\cap$ C)