The contrapositive of the inverse of p righta | vedclass

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(B) The inverse of a conditional statement $A \rightarrow B$ is $\sim A \rightarrow \sim B$. For the statement $p$ $\rightarrow (p$ $\rightarrow q)$,t

Vedclass · Accepted Answer

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

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(B) The inverse of a conditional statement $A \rightarrow B$ is $\sim A \rightarrow \sim B$. For the statement $p$ $\rightarrow (p$ $\rightarrow q)$,the inverse is $\sim p$ $\rightarrow \sim (p$ $\rightarrow q)$. The contrapositive of a conditional statement $A \rightarrow B$ is $\sim B \rightarrow \sim A$. Applying this to the inverse $\sim p$ $\rightarrow \sim (p$ $\rightarrow q)$,we get: $\sim [\sim (p$ $\rightarrow q)]$ $\rightarrow \sim (\sim p)$ $= (p$ $\rightarrow q)$ $\rightarrow p$ Since $p \rightarrow q \equiv \sim p \vee q$,the expression becomes $(\sim p \vee q) \rightarrow p$.

The contrapositive of the inverse of $p$ $\rightarrow (p$ $\rightarrow q)$ is

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