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 in 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, $p \land \sim q$ means "An integer is greater than $4$ and less than $5$ and it is not a multiple of $3$".Comparing this with the given options, option $(A)$ and $(D)$ represent the same logical statement. Since option $(A)$ is the standard form, it is the correct choice.

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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