The contrapositive of statement 'If Jaipur is capital of Rajasthan, then Jaipur is in India' is 

Which of the following  statements is $NOT$  logically equivalent to $\left( {p \to  \sim p} \right) \to \left( {p \to q} \right)$?

If the Boolean expression $( p \Rightarrow q ) \Leftrightarrow( q *(\sim p ))$ is a tautology, then the Boolean expression $p *(\sim q )$ is equivalent to

Consider

Statement $-1 :$$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$ is a fallacy.

Statement $-2 :$$(p \rightarrow q) \leftrightarrow ( \sim q \rightarrow   \sim  p )$  is a tautology.

The contrapositive of the statement “If you are born in India, then you are a citizen of India”, 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 ?