If the inverse of the conditional statement $p \to \left( { \sim q\ \wedge  \sim r} \right)$ is false, then the respective truth values of the statements $p, q$ and $r$ is

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is

If $\left( {p \wedge  \sim q} \right) \wedge \left( {p \wedge r} \right) \to  \sim p \vee q$ is false, then the truth values of $p, q$ and $r$ are respectively

The negation of the expression $q \vee((\sim q) \wedge p)$ is equivalent 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

The expression $ \sim ( \sim p\, \to \,q)$ is logically equivalent to