The contrapositive of "If x and y are integer | vedclass

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(D) Let $p$ be the statement: "$x$ and $y$ are integers such that $x y$ is odd".Let $q$ be the statement: "both $x$ and $y$ are odd".The given stateme

Vedclass · Accepted Answer

If $x$ and $y$ are not both odd,then $x y$ is not odd.

Vedclass · Answer

(D) Let $p$ be the statement: "$x$ and $y$ are integers such that $x y$ is odd".Let $q$ be the statement: "both $x$ and $y$ are odd".The given statement is $p \rightarrow q$.The contrapositive of $p \rightarrow q$ is $\sim q \rightarrow \sim p$.Here,$\sim q$ is "it is not the case that both $x$ and $y$ are odd",which means "$x$ and $y$ are not both odd".$\sim p$ is "$x y$ is not odd".Therefore,the contrapositive is "If $x$ and $y$ are not both odd,then $x y$ is not odd".Thus,option $D$ is correct.

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

Similar Questions

Which of the following statements is/are False?
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$S_2: \exists x \in N$, such that $x - 17 < 20$.
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