Question

Decide if the converse is true for the following true conditional statement: "If a number is divisible by 4, then it is even." If it is true, choose a valid biconditional statement.
A. A number is divisible by 4 if and only if it is even.
B. A number is even if and only if it is divisible by 4.
C. The converse is false. A valid biconditional cannot be formed.
D. A number is not even if and only if the number is not divisible by 4.

Answer 1

Answer:  The correct option is

(C) The converse is false. A valid bi conditional cannot be formed.

Step-by-step explanation:  We are given to decide whether the converse is true is TRUE for the following bi conditional statement :

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

And if it true, we are to choose a valid bi conditional statement.

Let us consider that

p : A number is divisible by 4

and

q : a number is even.

We know that the CONVERSE of the bi conditional statement p ⇒ q is given by q  ⇒  p.

So, the converse of the given bi conditional statement is

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

This statement is false, since there exists even numbers that are not divisible by 4.

For example, the number 6 is an even number but is ts not divisible by 4.

Thus, the CONVERSE is false and so a valid bi conditional statement cannot be formed.

Option (C) is CORRECT.

Answer 2

Decide if the converse is true for the following true conditional statement and the answer would be
B. A number is even if and only if it is divisible by 4.