Question

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? if a number has a negative cube root, then the number is negative. if a number does not have a negative cube root, then the number is not negative. if a number is negative, then it does not have a negative cube root. if a number is not negative, then it does not have a negative cube root.

Explanation:

First, recall the relationship between inverse, original, and contra - positive statements. The inverse of a conditional statement \(p
ightarrow q\) is \(
eg p
ightarrow
eg q\). Given the inverse "If a number is negative, then it has a negative cube root", the original conditional statement is "If a number is non - negative, then it has a non - negative cube root". The contra - positive of a conditional statement \(p
ightarrow q\) is \(
eg q
ightarrow
eg p\). So the contra - positive of the original statement is "If a number does not have a negative cube root, then the number is not negative".

Answer:

If a number does not have a negative cube root, then the number is not negative.