MHT CET · Maths · Mathematical Reasoning
The inverse of statement pattern \((p \vee q) \rightarrow(p \wedge q)\) is
- A \((\sim p \vee \sim q) \rightarrow(\sim p \wedge \sim q)\)
- B \((p \wedge q) \rightarrow(p \vee q)\)
- C \((p \wedge q) \rightarrow(p \vee q)\)
- D \(\sim(p \vee q) \rightarrow(p \wedge q)\)
Answer & Solution
Correct Answer
(B) \((p \wedge q) \rightarrow(p \vee q)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \because \text { inverse of } p \rightarrow q \text { is } \sim p \rightarrow \sim q \\ & \Rightarrow \text { inverse of } p \vee q \rightarrow p \wedge q \\ & \equiv \sim(p \vee q) \rightarrow \sim(p \wedge q) \\ & \equiv(\sim p \wedge \sim q) \rightarrow(\sim p \vee \sim q)\end{aligned}\)
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