The inverse of the statement pattern (p vee q | vedclass

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Question

(A) The inverse of a conditional statement $p \rightarrow q$ is defined as $\sim p \rightarrow \sim q$. Given the statement pattern $(p \vee q) \right

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The inverse of a conditional statement $p \rightarrow q$ is defined as $\sim p \rightarrow \sim q$. Given the statement pattern $(p \vee q) \rightarrow (p \wedge q)$,we identify $p$ as $(p \vee q)$ and $q$ as $(p \wedge q)$. Applying the definition,the inverse is $\sim(p \vee q) \rightarrow \sim(p \wedge q)$. Using De Morgan's laws,$\sim(p \vee q) \equiv (\sim p \wedge \sim q)$ and $\sim(p \wedge q) \equiv (\sim p \vee \sim q)$. Thus,the inverse is $(\sim p \wedge \sim q) \rightarrow (\sim p \vee \sim q)$.

The inverse of the statement pattern $(p \vee q) \rightarrow (p \wedge q)$ is

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