MHT CET · Maths · Mathematical Reasoning
The logical statement \((p \wedge \sim q) \vee q \vee(\sim p \wedge q)\) is equivalent to
- A \(p \vee \sim q\)
- B \(\sim p \wedge q\)
- C \(p \wedge q\)
- D \(p \vee q\)
Answer & Solution
Correct Answer
(D) \(p \vee q\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & (p \wedge \sim q) \vee q \vee(\sim p \wedge q) \\ & \equiv\{(p \wedge \sim q) \vee(\sim p \wedge q)\} \vee q \\ & \equiv \sim(p \Leftrightarrow q) \vee q \equiv p \vee q\end{aligned}\)
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