Question

If $x=6$ and $y=−2$ then $x−2y=9.$ The contrapositive of this statement is

• A. If $x−2yî€=9$ then $xî€=6$ or $yî€=−2$
• B. If $x−2yî€=9$ then $xî€=6$ and $yî€=−2$
• C. If $x−2y=9$ then $x=6$ and $y=−2$
• D. None of these

Answer 1

Answer: (A)

Let $p,q,r$ be the three statements such that
$p:x=6,q:y=−2$ and $r:x−2y=9$
Here given statement is $\left(pâˆ\S q\right)→r$ and its contrapositive is $∼r→∼\left(pâˆ\S q\right)$
i.e. $∼r→\left(∼p∨∼q\right)$
i.e. if $x−2yî€=9$ then $xî€=6$ or $yî€=−2$