Negation of the inverse of the following stat | vedclass

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(B) Let $S$ be the statement $(p \wedge q) \rightarrow (p \vee \sim q)$.The inverse of $S$ is $\sim(p \wedge q) \rightarrow \sim(p \vee \sim q)$.Using

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$\sim q$

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(B) Let $S$ be the statement $(p \wedge q) \rightarrow (p \vee \sim q)$.The inverse of $S$ is $\sim(p \wedge q) \rightarrow \sim(p \vee \sim q)$.Using the logical equivalence $A \rightarrow B \equiv \sim A \vee B$,the inverse is:$\sim[\sim(p \wedge q)] \vee \sim(p \vee \sim q)$$\equiv (p \wedge q) \vee (\sim p \wedge q)$ (By De Morgan's Law)$\equiv (q \wedge p) \vee (q \wedge \sim p)$ (By Commutative Law)$\equiv q \wedge (p \vee \sim p)$ (By Distributive Law)$\equiv q \wedge T$ (By Complement Law,where $T$ is a tautology)$\equiv q$ (By Identity Law).Now,the negation of the inverse is $\sim(q) = \sim q$.

Negation of the inverse of the following statement pattern $(p \wedge q) \rightarrow (p \vee \sim q)$ is

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