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

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 

The Boolean expression $( p \Rightarrow q ) \wedge( q \Rightarrow \sim p )$ is equivalent to :

Suppose $p, q, r$ are positive rational numbers such that $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is also rational. Then

The negation of $ \sim s \vee \left( { \sim r \wedge s} \right)$ is equivalent to :

The statement $( p \rightarrow( q \rightarrow p )) \rightarrow( p \rightarrow( p \vee q ))$ is