Question

The converse of the statement “if $p < q$, then $p - x < q - x$” is:
A. If $p < q$, then $p - x > q - x$
B. If $p > q$, then $p - x > q - x$
C. If $p - x > q - x$, then$p > q$
D. If $p - x < q - x$, then $p < q$

Answer 1

Hint: We can identify the hypothesis and conclusion of the given if statement. The converse of the statement can be found by interchanging the hypothesis and conclusion.

Complete step by step answer:

The given statement is an IF-THEN statement. It can be represented as if P then Q.
We have the statement, If $p < q$, then $p - x < q - x$
The statement after ‘if’ is called the hypothesis and the statement after then is the conclusion.
Here, $p < q$ is the hypothesis and $p - x < q - x$ is the conclusion. To find the converse of the statement, we interchange the hypothesis and the conclusion.
So the converse is given by, If $p - x < q - x$, then $p < q$
So the correct answer is option D.

Note: In mathematical logics statements are sentences which are either true or false. Let P and Q are two statements. Then “if P, then Q” means if P is true, then Q also will be true. Its converse is given by, “if Q, then P”. It means, if Q is true, then P will be true. For an, if statement, the converse need not be true.