If p, q, r are simple propositions with truth | vedclass

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(C) Given truth values: $p = T, q = F, r = T$.$(A)$ $[q \land (p 	o q)] 	o p = [F \land (T 	o F)] 	o T = [F \land F] 	o T = F 	o T = T$.$(B)$ $(

Vedclass · Accepted Answer

$[(\sim p \lor q) \land \sim r] \leftrightarrow p$

Vedclass · Answer

(C) Given truth values: $p = T, q = F, r = T$.$(A)$ $[q \land (p 	o q)] 	o p = [F \land (T 	o F)] 	o T = [F \land F] 	o T = F 	o T = T$.$(B)$ $(p \land q) 	o (q \lor \sim p) = (T \land F) 	o (F \lor \sim T) = F 	o (F \lor F) = F 	o F = T$.$(C)$ $[(\sim p \lor q) \land \sim r] \leftrightarrow p = [(\sim T \lor F) \land \sim T] \leftrightarrow T = [(F \lor F) \land F] \leftrightarrow T = [F \land F] \leftrightarrow T = F \leftrightarrow T = F$.$(D)$ $(p \land q) \lor (\sim q \lor r) = (T \land F) \lor (\sim F \lor T) = F \lor (T \lor T) = F \lor T = T$.Since option $(C)$ results in $F$, it is not a true statement.

If $p, q, r$ are simple propositions with truth values $T, F, T$ respectively, then which of the following is not a true statement?

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