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