The Boolean expression $\left( {\left( {p \wedge q} \right) \vee \left( {p \vee  \sim q} \right)} \right) \wedge \left( { \sim p \wedge  \sim q} \right)$ is equivalent to

The statement $p \rightarrow  (q \rightarrow p)$  is equivalent to

$\left( { \sim \left( {p \vee q} \right)} \right) \vee \left( { \sim p \wedge q} \right)$ is logically equivalent to 

Which of the following statement is a tautology?

Which of the following is a contradiction

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.