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 false.

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 ”

The square of a positive term is positive.

Therefore, the statement is true.

Consider p is and q 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.

If then x may be positive or negative. Thus, is also a possibility.

Therefore, the converse of the given statement is false.