If the truth value of [(p lor q) land (q to r | vedclass

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(C) The implication $A 	o B$ is false only when $A$ is true and $B$ is false.Step $1$: Set $[(p \lor q) \land (q 	o r) \land (\sim r)]$ to True and

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Truth value of $(\sim q) 	o p$ is False.

Vedclass · Answer

(C) The implication $A 	o B$ is false only when $A$ is true and $B$ is false.Step $1$: Set $[(p \lor q) \land (q 	o r) \land (\sim r)]$ to True and $(p \land q)$ to False.Step $2$: For the conjunction to be True, each part must be True: $(p \lor q) = T$, $(q 	o r) = T$, and $(\sim r) = T$.Step $3$: From $(\sim r) = T$, we get $r = F$. Since $(q 	o r) = T$ and $r = F$, $q$ must be $F$.Step $4$: Since $(p \lor q) = T$ and $q = F$, $p$ must be $T$.Step $5$: Check $(p \land q) = (T \land F) = F$, which is consistent.Step $6$: Evaluate options with $p=T, q=F, r=F$:$(A)$ $p 	o q = T 	o F = F$ (True statement)$(B)$ $p 	o r = T 	o F = F$ (True statement)$(C)$ $(\sim q) 	o p = (\sim F) 	o T = T 	o T = T$ (This is $NOT$ true, as it is True)$(D)$ $(\sim p) \land r = (\sim T) \land F = F \land F = F$ (True statement)Thus, option $(C)$ is the correct answer.

If the truth value of $[(p \lor q) \land (q \to r) \land (\sim r)] \to (p \land q)$ is false, then which of the following is $NOT$ true?

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