12
QuizMultiple Choice

Conditional Statements and Equivalence

Question 12 • FL-1206310-Geometry A - Flex

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?

Answer
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.

Explanation

The inverse of “If P, then Q” is “If not P, then not Q.” The given inverse says that if a number is negative, then it has a negative cube root, so the original statement is: if a number is not negative, then it does not have a negative cube root. Its contrapositive reverses the statements and negates both: if a number has a negative cube root, then the number is negative. That is choice C.

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