Conditional Statements and Equivalence Answers

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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.
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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.
3

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Question illustration
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.
4

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

A
~p → ~q
B
~q → ~p
C
q → p
D
p → ~q
5

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.
6

Which pairs of statements are logically equivalent? Select two options.the inverse and the contrapositive of the original conditional statementthe original conditional statement and its contrapositivethe original conditional statement and its inversethe converse and the inverse of the original conditional statementthe converse and the contrapositive of the original conditional statement

A
the inverse and the contrapositive of the original conditional statement
B
the original conditional statement and its contrapositive
C
the original conditional statement and its inverse
D
the converse and the inverse of the original conditional statement
E
the converse and the contrapositive of the original conditional statement
7

If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by ?

Question illustration
A
the original conditional statement
B
the inverse of the original conditional statement
C
the converse of the original conditional statement
D
the contrapositive of the original conditional statement
8

What is the contrapositive of the conditional statement?If two variables are directly proportional, then their graph is a linear function.

A
If two variables are directly proportional, then their graph is not a linear function.
B
If two variables are not directly proportional, then their graph is not a linear function.
C
If the graph of two variables is a linear function, then the two variables are directly proportional.
D
If the graph of two variables is not a linear function, then the two variables are not directly proportional.
9

Given:p: x – 5 =10q: 4x + 1 = 61Which is the inverse of p → q?

A
If x – 5 ≠ 10, then 4x + 1 ≠ 61.
B
If 4x + 1 ≠ 61, then x – 5 ≠ 10.
C
If x – 5 = 10, then 4x + 1 = 61.
D
If 4x + 1 = 61, then x – 5 = 10.
10

If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by ~p → ~q?

A
the original conditional statement
B
the converse of the original conditional statement
C
the contrapositive of the original conditional statement
D
the inverse of the original conditional statement

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