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Question: Answered & Verified by Expert
The inverse of the proposition $(p \wedge-q) \Rightarrow r$ is
MathematicsMathematical ReasoningMHT CETMHT CET 2011
Options:
  • 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
Solution:
1321 Upvotes Verified Answer
The correct answer is: $\sim p \vee q \Rightarrow \sim r$
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., $\quad(\sim p \vee q) \Rightarrow \wedge \sim r$

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