UGC NET CSE | October 2022 | Part 1 | Question: 37

Question

The logic expression $(\bar{P} \wedge Q) \vee(P \wedge \bar{Q}) \vee(P \wedge Q)$ is equivalent to

• A. $\bar{P} \vee Q$,
• B. $P \vee \bar{Q}$
• C. $P \vee Q$
• D. $\bar{P} \vee \bar{Q}$

Answer 1

In mathematical logic $\wedge$ represents an AND,$\vee$ represents an OR logic, based on that we can rewrite the given expression:

$(\bar P \wedge Q)\vee(P\wedge \bar Q\vee(P\wedge Q))$

$\implies\bar PQ+P\bar Q+PQ$
$\implies Q(P+\bar P)+P\bar Q$
$\implies Q+P\bar Q$
$\implies(P+Q)(Q+\bar Q)$ (Apply distributive law, $\because A+\bar A=1$)
$\implies (P+Q)\equiv P\vee Q$

Option (C) is correct.