Question

Which of the following biconditional statements is true?

The product of two integers is negative if and only if both of its factors are negative.


A whole number is divisible by 4 if and only if it is divisible by 2.


A whole number is even if and only if it is evenly divisible by 2.


A whole number is odd if and only if it is evenly divisible by 2.

Answer 1

It would have to be the even only if divisible by 2

Answer 2

A whole number is even if and only if it is evenly divisible by 2

Explanation:

1. The first statement is false because product of two negative integers is positive.

Ex:

(- 2) × (- 3) = 6

2. The second statement is false because there are whole numbers which are divisible by 2 but not divisible by 4.

Ex:

6 is divisible by 2 but not divisible by 4

3. The fourth statement is false because if a whole number is divisible by 2, then, by definition, it must be an even number.

Ex:

6 is divisible by 2 and hence it is an even number

4. The third statement is true because if a whole number is divisible by 2, then, by definition, it must be an even number.

Ex:

6 is divisible by 2 and hence it is an even number