Contrapositive of $x=2, y=3,$ then $xy=6$

Question

Help in writing contraposition for this statement

Answer 1

The contrapositive of a statement $P \rightarrow Q$ is $\lnot Q \rightarrow \lnot P$. In words, if $P$ then $Q$ has a contrapositive that reads if not $Q$, then not $P$.

Your statement is if ($x=2$ and $y=3$), then $(xy=6)$. The contrapositive is, using the form above, if $\lnot(xy=6)$, then $\lnot (x=2 \text{ and }y=3)$. In other words, if $xy\neq 6$, then we cannot have $x=2$ and $y=3$ --- if we did, then $xy=6$, and that would be a contradiction. So the contrapositive is true.