The inverse of the proposition $(p\; \wedge \sim q) \Rightarrow r$ 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

Similar Questions

Which one of the following, statements is not a tautology

  • [JEE MAIN 2019]

Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ be four non-empty sets. The contrapositive statement of "If $\mathrm{A} \subseteq \mathrm{B}$ and $\mathrm{B} \subseteq \mathrm{D},$ then $\mathrm{A} \subseteq \mathrm{C}^{\prime \prime}$ is 

  • [JEE MAIN 2020]

Which of the following Boolean expression is a tautology ?

  • [JEE MAIN 2021]

Statement $p$ $\rightarrow$  ~$q$ is false, if

Statement$-I :$  $\sim (p\leftrightarrow q)$ is equivalent to $(p\wedge \sim  q)\vee \sim  (p\vee \sim  q) .$
Statement$-II :$  $p\rightarrow (p\rightarrow q)$ is a tautology.