What is the inverse of the following conditional statement?

Question

"If a number is a prime number, then it has no factors other than one and itself."

If a number is not a prime number, then it has factors other than one and itself.

 If a number has no factors other than one and itself, then it is a prime number. 

A number is a prime number if and only if it has no factors other than one and itself. 

If a number has factors other than one and itself, then it is not a prime number.

Answer 1

Hello, An inverse of a conditional statement is the negation of the hypothesis and conclusion.. in this case we need the negative of both parts of the statement.

For example, If the statement is "If X, then Y", the inverse would be "If not X, then not Y".

The statement is "If a number is a prime number, then it has no factors other than one and itself".

The inverse of this statement would need to be.... "If a number is not a prime number, then it has factors other than once and itself"

I hope this is helpful.