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.$1$. Let $A = (p \lor q) \land (q 	o r) \land (\sim r)$ be True and $B

Vedclass · Accepted Answer

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.$1$. Let $A = (p \lor q) \land (q 	o r) \land (\sim r)$ be True and $B = (p \land q)$ be False.$2$. For $A$ to be True, $(p \lor q)$, $(q 	o r)$, and $(\sim r)$ must all be True.$3$. Since $(\sim r)$ is True, $r$ is False.$4$. Since $(q 	o r)$ is True and $r$ is False, $q$ must be False.$5$. Since $(p \lor q)$ is True and $q$ is False, $p$ must be True.$6$. Check $B = (p \land q) = (T \land F) = False$. This matches our condition.$7$. Evaluate options:$(a)$ $p 	o q = T 	o F = False$. (True statement)$(b)$ $p 	o r = T 	o F = False$. (True statement)$(c)$ $(\sim q) 	o p = (\sim F) 	o T = T 	o T = True$. (This is $NOT$ true as it is True)$(d)$ $(\sim p) \land r = (\sim T) \land F = F \land F = False$. (True statement)Therefore, 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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