The inverse of the proposition $(p\; \wedge \sim q) \Rightarrow r$ is
$\sim r \Rightarrow\;\sim p \vee q$
$\sim p \vee q \Rightarrow \;\sim r$
$r \Rightarrow p\; \wedge \sim q$
None of these
Which one of the following, statements is not a tautology
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
Which of the following Boolean expression is a tautology ?
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.