The contrapositive of (sim p wedge q) rightar | vedclass

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Question

(D) The contrapositive of a conditional statement $p \rightarrow q$ is defined as $\sim q \rightarrow \sim p$. Given the statement $(\sim p \wedge q)

Vedclass · Accepted Answer

$(\sim q \vee r) \rightarrow (p \vee \sim q)$

Vedclass · Answer

(D) The contrapositive of a conditional statement $p \rightarrow q$ is defined as $\sim q \rightarrow \sim p$. Given the statement $(\sim p \wedge q) \rightarrow (q \wedge \sim r)$,we identify $p$ as $(\sim p \wedge q)$ and $q$ as $(q \wedge \sim r)$. The contrapositive is $\sim (q \wedge \sim r) \rightarrow \sim (\sim p \wedge q)$. Applying De Morgan's Laws: $\sim (q \wedge \sim r) \equiv \sim q \vee \sim (\sim r) \equiv \sim q \vee r$. $\sim (\sim p \wedge q) \equiv \sim (\sim p) \vee \sim q \equiv p \vee \sim q$. Thus,the contrapositive is $(\sim q \vee r) \rightarrow (p \vee \sim q)$.

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

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