Among the statements:

$(S1)$ $\quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow( p \Rightarrow r )$

$(S2) \quad(( p \vee q ) \Rightarrow r ) \Leftrightarrow(( p \Rightarrow r ) \vee( q \Rightarrow r ))$

Consider the statement "The match will be played only if the weather is good and ground is not wet". Select the correct negation from the following:

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

Which Venn diagram represent the truth of the statement“Some teenagers are not dreamers”

Consider the statement : "For an integer $n$, if $n ^{3}-1$ is even, then $n$ is odd." The contrapositive statement of this statement is

The converse of the statement $((\sim p) \wedge q) \Rightarrow r$ is