Question

State the converse of each conditional. Is the converse true or false?

If , then .

Short answer

The converse of the given statement is "If then ” and the converse is True.

Step-by-step solution

Step 1. Converse of 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 the converse of the statement.

"If , then ”

Here

Then

Therefore, the statement is true.

Consider p is “” and is “”.

The converse is of the form "If q, then p”.

Therefore, the converse of the given statement is:

If , then .

Step 3. Verify the converse of the statement.

In order to prove the converse of the statement:

Putintoand simplify:

Therefore, the converse of the given statement is true.