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The negation of the proposition "If 2 is prime, then 3 is odd'" is
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2 is prime and 3 is not odd
Let $p=2$ is prime
$q=3$ is odd
$p \rightarrow q=2$ is prime, then 3 is odd.
Negation of $P \rightarrow q$ is $\sim(p \rightarrow q)$
$\Rightarrow \quad p \wedge \sim q$
$\Rightarrow 2$ is prime and 3 is not odd.
$q=3$ is odd
$p \rightarrow q=2$ is prime, then 3 is odd.
Negation of $P \rightarrow q$ is $\sim(p \rightarrow q)$
$\Rightarrow \quad p \wedge \sim q$
$\Rightarrow 2$ is prime and 3 is not odd.
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