The negation of the statement "If an integer | vedclass

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Question

(A) Let $P$ be the statement "An integer is greater than $4$ and less than $5$" and $Q$ be the statement "It is a multiple of $3$".The given statement

Vedclass · Accepted Answer

An integer is greater than $4$ and less than $5$ and it is not a multiple of $3$.

Vedclass · Answer

(A) Let $P$ be the statement "An integer is greater than $4$ and less than $5$" and $Q$ be the statement "It is a multiple of $3$".The given statement is of the form "If $P$, then $Q$", which is denoted as $P \implies Q$.The negation of $P \implies Q$ is $\sim(P \implies Q) \equiv P \land \sim Q$.Here, $P$ is "An integer is greater than $4$ and less than $5$" and $\sim Q$ is "It is not a multiple of $3$".Therefore, the negation is "An integer is greater than $4$ and less than $5$ and it is not a multiple of $3$".

The negation of the statement "If an integer is greater than $4$ and less than $5$, then it is a multiple of $3$" is:

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