The statement $p → (p \leftrightarrow  q)$ is logically equivalent to :-

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

Consider the two statements :

$(\mathrm{S} 1):(\mathrm{p} \rightarrow \mathrm{q}) \vee(\sim \mathrm{q} \rightarrow \mathrm{p})$ is a tautology

$(S2): (\mathrm{p} \wedge \sim \mathrm{q}) \wedge(\sim \mathrm{p} \vee \mathrm{q})$ is a fallacy.

Then :

If the Boolean expression $( p \wedge q ) \circledast( p \otimes q )$ is a tautology, then $\circledast$ and $\otimes$ are respectively given by

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?