The inverse of p rightarrow (q rightarrow r) | vedclass

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Question

(D) The inverse of a conditional statement $A \rightarrow B$ is defined as $\sim A \rightarrow \sim B$. For the statement $p$ $\rightarrow (q$ $\right

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) The inverse of a conditional statement $A \rightarrow B$ is defined as $\sim A \rightarrow \sim B$. For the statement $p$ $\rightarrow (q$ $\rightarrow r)$,the inverse is $\sim p$ $\rightarrow \sim (q$ $\rightarrow r)$. Using the property that $\sim (q \rightarrow r) \equiv q \wedge \sim r$,this does not immediately match the options. However,let us re-examine the logical equivalence. Given $p$ $\rightarrow (q$ $\rightarrow r)$,the inverse is $\sim p$ $\rightarrow \sim (q$ $\rightarrow r)$. Using the contrapositive rule,$\sim A$ $\rightarrow \sim B \equiv B$ $\rightarrow A$. Let $A = p$ and $B = (q \rightarrow r)$. Then $\sim p$ $\rightarrow \sim (q$ $\rightarrow r) \equiv (q$ $\rightarrow r)$ $\rightarrow p$. Thus,the inverse is logically equivalent to $(q$ $\rightarrow r)$ $\rightarrow p$.

The inverse of $p$ $\rightarrow (q$ $\rightarrow r)$ is logically equivalent to

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