$( S 1)( p \Rightarrow q ) \vee( p \wedge(\sim q ))$ is a tautology $( S 2)((\sim p ) \Rightarrow(\sim q )) \wedge((\sim p ) \vee q )$ is a Contradiction. Then

The negation of $ \sim s \vee \left( { \sim r \wedge s} \right)$ is equivalent to :

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

Negation of "If India wins the match then India will reach in the final" is :-

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

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