The Boolean expression $\left( {\left( {p \wedge q} \right) \vee \left( {p \vee \sim q} \right)} \right) \wedge \left( { \sim p \wedge \sim q} \right)$ is equivalent to
$p \wedge q$
$p \wedge \left( { \sim q} \right)$
$\left( { \sim p} \right) \wedge \left( { \sim q} \right)$
$p \vee \left( { \sim q} \right)$
The negation of the compound proposition $p \vee (\sim p \vee q)$ is
The contrapositive of the statement "If I reach the station in time, then I will catch the train" is
$( S 1)( p \Rightarrow q ) \vee( p \wedge(\sim q ))$ is a tautology $( S 2)((\sim p ) \Rightarrow(\sim q )) \wedge((\sim p ) \vee q )$ is a Contradiction. Then
The false statement in the following is
If $p , q$ and $r$ are three propositions, then which of the following combination of truth values of $p , q$ and $r$ makes the logical expression $\{(p \vee q) \wedge((\sim p) \vee r)\} \rightarrow((\sim q) \vee r)$ false ?