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What is the negation of the compound statement (p ^ ~q)?

May 27, 2026Mathematics

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1. The negation of the compound statement $(p \wedge \sim q)$ is

Apply De Morgan's Law to the given statement.
The negation of $(p \wedge \sim q)$ is $\sim (p \wedge \sim q)$ .
According to De Morgan's Law, $\sim (A \wedge B) \equiv \sim A \vee \sim B$ .
Here, $A = p$ and $B = \sim q$ .
Substitute $A$ and $B$ into De Morgan's Law.
$\sim (p \wedge \sim q) \equiv \sim p \vee \sim (\sim q)$

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