Using the mathematical reasoning, what will be the converse of the following statement : 'if \(x<y\), then \(x+5<y+5\)', where \(x\) and \(y\) are positive integers ?
If \(x+5<y+5\), then \(x<y\)
The given statement is: if \(x<y\), then \(x+5<y+5\), which has the form "if P, then Q".
The converse of a conditional statement "if P, then Q" is formed by interchanging the hypothesis and the conclusion, giving "if Q, then P".
Here, P is \(x<y\) and Q is \(x+5<y+5\), so the converse becomes: if \(x+5<y+5\), then \(x<y\).
Hence, the converse of the given statement is: if \(x+5<y+5\), then \(x<y\).
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