Question

What is the inverse of the statement?

A number that has exactly two distinct factors is prime.
OIf a number has exactly two distinct factors, then the number is prime.
O If a number does not have exactly two distinct factors, then the number is not prime.
O If a number is not prime, then the number does not have exactly two distinct factors.
O If a number is prime, then the number has exactly two distinct factors.

Answer 1

The inverse of the statement "A number that has exactly two distinct factors is prime" is:

"If a number does not have exactly two distinct factors, then the number is not prime."

Therefore, the correct option is:

O If a number does not have exactly two distinct factors, then the number is not prime.

Explanation:

The inverse of the statement "A number that has exactly two distinct factors is prime" is:

"If a number does not have exactly two distinct factors, then the number is not prime."

Therefore, the correct option is:

O If a number does not have exactly two distinct factors, then the number is not prime.

Answer 2

If a statement is of the form "If p, then q", the inverse of the statement is "If not p, then not q".

The statement "A number that has exactly two distinct factors is prime" can be written as "If a number has exactly two distinct factors, then the number is prime".

The inverse of this statement is "If a number does not have exactly two distinct factors, then the number is not prime".

Therefore, the answer is O If a number does not have exactly two distinct factors, then the number is not prime.