The contrapositive of "If $x$ and $y$ are integers such that $x y$ is odd, then both $x$ and $y$ are odd" is
The contrapositive of "If $x$ and $y$ are integers such that $x y$ is odd, then both $x$ and $y$ are odd" is
If both $x$ and $y$ are odd integers, then $x y$ is odd.
If both $x$ and $y$ are even integers, then $x y$ is even.
If $x$ or $y$ is an odd integer, then $x y$ is odd.
If both $x$ and $y$ are not odd integers, then the product $x y$ is not odd.
Solution
Let $\mathrm{p}: x$ and $y$ are integers such that $x y$ is odd. $\mathrm{q}:$ both $x$ and $y$ are odd.
$\therefore \quad$ Given statement is $\mathrm{p} \rightarrow \mathrm{q}$
$\therefore \quad$ Its contrapositive is $\sim q \rightarrow p$
$\therefore \quad$ Option (D) is correct.