If p, q and r are three propositions,then whi | vedclass

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(C) conditional statement $A \rightarrow B$ is false only when $A$ is True and $B$ is False.Let $A = (p \vee q) \wedge ((\sim p) \vee r)$ and $B = ((\

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$p = F, q = T, r = F$

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(C) conditional statement $A \rightarrow B$ is false only when $A$ is True and $B$ is False.Let $A = (p \vee q) \wedge ((\sim p) \vee r)$ and $B = ((\sim q) \vee r)$.We need to find the case where $A = T$ and $B = F$.For $B = ((\sim q) \vee r)$ to be False,both $(\sim q)$ and $r$ must be False.This implies $q = T$ and $r = F$.Now,substitute $q = T$ and $r = F$ into $A = (p \vee q) \wedge ((\sim p) \vee r)$:$A = (p \vee T) \wedge ((\sim p) \vee F)$$A = T \wedge (\sim p)$For $A$ to be True,$(\sim p)$ must be True,which means $p = F$.Thus,the combination $p = F, q = T, r = F$ makes the expression False.

If $p, q$ and $r$ are three propositions,then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression $\{(p \vee q) \wedge ((\sim p) \vee r)\} \rightarrow ((\sim q) \vee r)$ false?

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