Question

Use the conditional statement to answer the question.

If a whole number is even, then the number is divisible by 4.



Are the statement and its converse true?

Responses

Both the statement and its converse are false.
Both the statement and its converse are false.

The statement is true, but the converse is false.
The statement is true, but the converse is false.

The statement is false, but the converse is true.
The statement is false, but the converse is true.

Both the statement and its converse are true.

Answer 1

The statement is false, but the converse is true.

Explanation:

Statement:

"If a whole number is even, then the number is divisible by 4."

Counterexample: 2 is even. 2 is not divisible by 4.

The statement is false.

Converse:

"If a whole number is divisible by 4, then the number is even."

The converse is true since for a number to be even, it has to have at least one prime factor of 2, and every number that is divisible by 4 has at least 2 prime factors of 2.

Answer: The statement is false, but the converse is true.