Q92 / 150 · MHT CET 2023 (12 May Shift 1) · Mathematics

The contrapositive of "If $x$ and $y$ are integers such that $x y$ is odd, then both $x$ and $y$ are odd" is

  • A
    If both $x$ and $y$ are odd integers, then $x y$ is odd.
  • B
    If both $x$ and $y$ are even integers, then $x y$ is even.
  • C
    If $x$ or $y$ is an odd integer, then $x y$ is odd.
  • Correct answer
    D
    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.

Hence, the correct answer is option: 'D'.

Relevant Questions