The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to 

Consider the following three statements :
$P : 5$ is a prime number.
$Q : 7$ is a factor of $192$.
$R : L.C.M.$ of $5$ and $7$ is $35$.
Then the truth value of which one of the following statements is true?

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

Consider

Statement $-1 :$$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.

Statement $-2 :$$(p \rightarrow q) \leftrightarrow ( \sim q \rightarrow   \sim  p )$  is a tautology.

The statement $( p \wedge q ) \Rightarrow( p \wedge r )$ is equivalent to.