Question

Give an example of a false conditional whose converse is true.

Short answer

A false conditional whose converse is true is “A number is divisible by 2, then it is divisible by 8.”

Step-by-step solution

Step 1. Converse a conditional.

The converse of the conditional is obtained by interchanging the hypothesis and the conclusion. If p represents the hypothesis and q represents the conclusion, then converse of the statement “If p, then q” will be “If q, then p”.

Step 2. Write a false conditional.

In order to find a false conditional, consider a statement that is not true.

Let "A number is divisible by 2, then it is divisible by 8”.

Consider the number 10

It is divisible by 2 but not by 8

Therefore, the statement is false

Step 3. Write the converse of the false conditional.

Consider p is "a number is divisible by 2” and q is "it is divisible by 8”

The converse is of the form "if p, then p”

Therefore, the converse of the given statement is- “If a number is divisible by 8, then it is divisible by 2.”

Also, every number which is divisible by 8 is also divisible by 2. Therefore, the converse of the given statement is true.

Therefore, a false conditional whose converse is true is “A number is divisible by 2, then it is divisible by 8.”