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

$\sim ((\sim p)\; \wedge q)$ is equal to

Consider the following two propositions:

$P_1: \sim( p \rightarrow \sim q )$

$P_2:( p \wedge \sim q ) \wedge((\sim p ) \vee q )$

If the proposition $p \rightarrow((\sim p ) \vee q )$ is evaluated as $FALSE$, then

If $\mathrm{p} \rightarrow(\mathrm{p} \wedge-\mathrm{q})$ is false, then the truth values of $p$ and $q$ are respectively