The negation of the statement (p wedge q) rig | vedclass

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

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$p \wedge q \wedge \sim r$

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(C) To find the negation of the statement $(p \wedge q) \rightarrow (\sim p \vee r)$,we use the logical equivalence $\sim(A \rightarrow B) \equiv A \wedge \sim B$.Let $A = (p \wedge q)$ and $B = (\sim p \vee r)$.Then,$\sim(A \rightarrow B) \equiv (p \wedge q) \wedge \sim(\sim p \vee r)$.Applying De Morgan's Law,$\sim(\sim p \vee r) \equiv \sim(\sim p) \wedge \sim r \equiv p \wedge \sim r$.So,the expression becomes $(p \wedge q) \wedge (p \wedge \sim r)$.By the Associative and Idempotent Laws,$(p \wedge q) \wedge p \wedge \sim r \equiv p \wedge q \wedge \sim r$.

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

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Statement-$1$: $\sim (p \Leftrightarrow \sim q)$ is equivalent to $p \Leftrightarrow q$.
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