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Question: Answered & Verified by Expert
The negation of the logical statement $(\mathrm{p} \vee \sim \mathrm{q}) \rightarrow(\mathrm{p} \wedge \sim \mathrm{q})$ is
MathematicsMathematical ReasoningMHT CETMHT CET 2020 (20 Oct Shift 1)
Options:
  • A $(p \wedge \sim q) \wedge(p \vee \sim q)$
  • B $(p \vee \sim q) \wedge(\sim p \vee q)$
  • C $(p \vee \sim q) \wedge(p \wedge q)$
  • D $(p \vee \sim q) \vee(\sim p \wedge q)$
Solution:
1557 Upvotes Verified Answer
The correct answer is: $(p \vee \sim q) \wedge(\sim p \vee q)$
$\sim[p \vee \sim q \rightarrow(p \wedge \sim q)]$
$\equiv \sim \sim(p \vee \sim q) \vee(p \wedge \sim q)]$
$\equiv(p \vee \sim q) \wedge \sim(p \wedge \sim q)$
$\equiv(p \vee \sim q) \wedge(\sim p \vee q)$

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