Use the conditional statement to answer the question.

If a number is a prime number, then the number is odd.

Can the statement be written as a biconditional statement and why?

A. Yes, because the statement and its converse are both true

B. No, because the statement is false, but its converse is true

C. No, because the statement is true, but its converse is false

D. No, because the statement and its converse are both false

the answer is D

We have been given a conditional statement and we are asked to find out whether this statement can be written as a bi-conditional statement or not.

First of all we will see what a bi-conditional statement is? A bi-conditional statement is a statement when the statement and its converse both are true. The first part of the statement tells a hypothesis and the last part tells us the conclusion of that hypothesis.

Since we know that 2 is a prime number and its not odd, so our given statement is false.

Now look at the converse of this statement. We can see by counter example of 9 that 9 is an odd number but it is not prime number.

Therefore, option D is the correct choice.