Question

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

• A. If $x-2y\neq 9$ then $x\neq 6$ or $y\neq -2$
• B. If $x-2y\neq 9$ then $x\neq 6$ and $y\neq -2$
• 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 $\left(p \land q\right) \rightarrow r$ and its contrapositive is $\sim r \rightarrow \sim \left(p \land q\right)$
i.e. $\sim r \rightarrow \left(\sim p \lor \sim q\right)$
i.e. if $x-2y\neq 9$ then $x\neq 6$ or $y\neq -2$