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Question: Answered & Verified by Expert
The logical statement $(p \wedge \sim q) \vee q \vee(\sim p \wedge q)$ is equivalent to
MathematicsMathematical ReasoningMHT CETMHT CET 2022 (05 Aug Shift 1)
Options:
  • A $p \vee \sim q$
  • B $\sim p \wedge q$
  • C $p \wedge q$
  • D $p \vee q$
Solution:
1102 Upvotes Verified Answer
The correct answer is: $p \vee q$
$\begin{aligned} & (p \wedge \sim q) \vee q \vee(\sim p \wedge q) \\ & \equiv\{(p \wedge \sim q) \vee(\sim p \wedge q)\} \vee q \\ & \equiv \sim(p \Leftrightarrow q) \vee q \equiv p \vee q\end{aligned}$

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