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Conditional Statements and Equivalence Answers

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Given a conditional statement p → q, which statement is logically equivalent?

A
~p → ~q
B
~q → ~p
C
q → p
D
p → ~q
2
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What is the inverse of the statement?A number that has exactly two distinct factors is prime.

A
If a number has exactly two distinct factors, then the number is prime.
B
If a number does not have exactly two distinct factors, then the number is not prime.
C
If a number is not prime, then the number does not have exactly two distinct factors.
D
If a number is prime, then the number has exactly two distinct factors.
3

Given:p: 2x = 16q: 3x – 4 = 20Which is the converse of p → q?

A
If 2x ≠ 16, then 3x – 4 ≠ 20.
B
If 3x – 4 ≠ 20, then 2x ≠ 16.
C
If 2x = 16, then 3x – 4 = 20.
D
If 3x – 4 = 20, then 2x = 16.
4

Given the original statement "If a number is negative, the additive inverse is positive,” which are true? Select three options.

A
If p = a number is negative and q = the additive inverse is positive, the original statement is p → q.
B
If p = a number is negative and q = the additive inverse is positive, the inverse of the original statement is ~p → ~q.
C
If p = a number is negative and q = the additive inverse is positive, the converse of the original statement is ~q → ~p.
D
If q = a number is negative and p = the additive inverse is positive, the contrapositive of the original statement is ~p → ~q.
E
If q = a number is negative and p = the additive inverse is positive, the converse of the original statement is q → p.
5

Given:p: Two linear functions have different coefficients of x.q: The graphs of two functions intersect at exactly one point. Which statement is logically equivalent to q → p?

A
If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one point.
B
If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect at exactly one point.
C
If the graphs of two functions do not intersect at exactly one point, then the two linear functions have the same coefficients of x.
D
If the graphs of two functions intersect at exactly one point, then the two linear functions have the same coefficients of x.
6

The inverse of a conditional statement is "If a number is negative, then it has a negative cube root.”What is the contrapositive of the original conditional statement?

A
If a number is negative, then it does not have a negative cube root.
B
If a number does not have a negative cube root, then the number is not negative.
C
If a number has a negative cube root, then the number is negative.
D
If a number is not negative, then it does not have a negative cube root.
7

What is the converse of the conditional statement?If x is even, then x + 1 is odd.

A
If x is not even, then x + 1 is not odd.
B
If x + 1 is odd, then x is even.
C
If x + 1 is not odd, then x is not even.
D
If x is even, then x + 1 is not odd.
8

Given the conditional statement ~p → q, which statement is logically equivalent?

A
p → ~q
B
~p → ~q
C
~q → ~p
D
~q → p
9

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A
If a number is prime, it is also odd.
B
If a number is odd, it is also prime.
C
If a number is not odd, it cannot be prime.
D
If a number is prime, it may or may not be odd.

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