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?

Both the statement and its converse are false.

The statement is true, but the converse is false.

The statement is false, but the converse is true.

Both the statement and its converse are true.

Answer 1

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

Answer:
If a whole number is even, then the number is divisible by 4.
This statement is false because there are even numbers smaller than 4 that are not divisible by 4.

The converse of the statement is If a number is divisible by 4, then the number is even.
This statement is true because all multiples of 4 are even.

Answer 2

Answer: the correct option is

(C) The statement is false, but the converse is true.

Step-by-step explanation: we are given to check whether the following conditional statement and its converse true :

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

Let us consider that

p : a whole number is even

and

q : the number is divisible by 4.

The conditional statement is "p ⇒ q".

Let us take an even number, for example 6. Here, we see that the whole number 6 is even but it is not divisible by 4.

So, the given statement is FALSE.

Now, the converse of "p ⇒ q" is "q ⇒ p".

That is, if a whole number is divisible by 4, then it is even.

This is true, because if a number is divisible by 4, then it must be divisible by 2. That means the number is even.

So, the converse is TRUE.

Thus, the given statement is FALSE but its converse is TRUE.

Option (C) is CORRECT.