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