Q97 / 150 · MHT CET 2011 · Mathematics

The inverse of the proposition $(p \wedge-q) \Rightarrow r$ is

  • A
    $\sim r \Rightarrow \sim p \vee q$
  • Correct answer
    B
    $\sim p \vee q \Rightarrow \sim r$
  • C
    $r \Rightarrow p \wedge \sim q$
  • D
    None of these

Solution

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., $\quad(\sim p \vee q) \Rightarrow \wedge \sim r$

Hence, the correct answer is option: 'B'.

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