MHT CET · Maths · Mathematical Reasoning
The negation of the statement pattern \(p v(q \rightarrow \sim r)\) is
- A \(\sim p \wedge(\sim q \wedge r)\)
- B \(\sim p \wedge(\sim q \wedge \sim r)\)
- C \(\sim p \wedge(q \wedge \sim r)\)
- D \(\sim p \wedge(q \wedge r)\)
Answer & Solution
Correct Answer
(D) \(\sim p \wedge(q \wedge r)\)
Step-by-step Solution
Detailed explanation
\(\sim\{p \vee(q \rightarrow \sim r)\} \equiv \sim p \wedge \sim(q \rightarrow \sim r)[\because \sim(p \rightarrow q) \equiv\) \( p \wedge \sim q] \)
\( \equiv \sim p \wedge(q \wedge \sim(\sim r)) \)
\( \equiv \sim p \wedge(q \wedge r)\)
\( \equiv \sim p \wedge(q \wedge \sim(\sim r)) \)
\( \equiv \sim p \wedge(q \wedge r)\)
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