The negation of (p wedge q) rightarrow (sim p | vedclass

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(D) To find the negation of the implication $(p \wedge q) \rightarrow (\sim p \vee r)$,we use the logical equivalence $\sim(A \rightarrow B) \equiv A

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$p \wedge q \wedge (\sim r)$

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(D) To find the negation of the implication $(p \wedge q) \rightarrow (\sim p \vee r)$,we use the logical equivalence $\sim(A \rightarrow B) \equiv A \wedge \sim B$. Let $A = (p \wedge q)$ and $B = (\sim p \vee r)$. The negation is $\sim(A \rightarrow B) \equiv A \wedge \sim B$. Substituting the values: $(p \wedge q) \wedge \sim(\sim p \vee r)$ Using De Morgan's Law,$\sim(\sim p \vee r) \equiv \sim(\sim p) \wedge \sim r \equiv p \wedge \sim r$. Therefore,the expression becomes: $(p \wedge q) \wedge (p \wedge \sim r)$ By the associative and idempotent laws,this simplifies to: $p \wedge q \wedge (\sim r)$.

The negation of $(p \wedge q) \rightarrow (\sim p \vee r)$ is

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