How can this inverse of conditional statement be equivalent? "A positive integer is a prime only if it has no divisors other than one and itself." The inverse of this conditional statement is : " A positive integer is not prime if it has divisors other than one and itself."
In logic the inverse isn't equivalent to the original statement. Can someone please clarify it for me??

I believe you are going wrong with words. From Rosen's Discrete Mathematics, $p \rightarrow q$, can be expressed this way:


*

*$p$ only if $q$.

*$q$ if $p$.
It means that if your first statement is $p \rightarrow q$, your second statement is actually $\neg q\rightarrow \neg p$ (contrapositive), not $\neg p\rightarrow \neg q$ (inverse).
