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QuizMultiple Choice

Conditional Statements and Equivalence — Quiz

Question 1 • MASTER COURSE Geometry

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 does not have a negative cube root, then the number is not negative.
B
If a number is negative, then it does not have a negative cube root.
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 reverses neither the order nor the direction of the conditional; it negates both parts. So the original statement is: If a number is not negative, then it does not have a negative cube root. The contrapositive switches the parts and negates both, giving: If a number has a negative cube root, then the number is negative. That is choice C.

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