MHT CET · Maths · Mathematical Reasoning
The inverse of the proposition \((p \wedge-q) \Rightarrow r\) is
- A \(\sim r \Rightarrow \sim p \vee q\)
- B \(\sim p \vee q \Rightarrow \sim r\)
- C \(r \Rightarrow p \wedge \sim q\)
- D None of these
Answer & Solution
Correct Answer
(B) \(\sim p \vee q \Rightarrow \sim r\)
Step-by-step Solution
Detailed explanation
Inverse of \(p \Rightarrow q\) is \(\sim p \Rightarrow \sim q\)
\(\therefore\) Inverse of \((p \wedge \sim q) \Rightarrow \mathrm{r}\) is
\(
\sim(p \wedge \sim q) \Rightarrow \sim r
\)
i.e., \(\quad(\sim p \vee q) \Rightarrow \wedge \sim r\)
\(\therefore\) Inverse of \((p \wedge \sim q) \Rightarrow \mathrm{r}\) is
\(
\sim(p \wedge \sim q) \Rightarrow \sim r
\)
i.e., \(\quad(\sim p \vee q) \Rightarrow \wedge \sim r\)
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