The statement $p → (p \leftrightarrow q)$ is logically equivalent to :-
$(p → q) \vee (q → p)$
$(p → q) \wedge (q →p)$
$(q→ p) → (p → q)$
$(q → p) \leftrightarrow (p →q)$
The logical statement $[ \sim \,( \sim \,P\, \vee \,q)\, \vee \,\left( {p\, \wedge \,r} \right)\, \wedge \,( \sim \,q\, \wedge \,r)]$ is equivalent to
The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is
The proposition $\left( { \sim p} \right) \vee \left( {p\, \wedge \sim q} \right)$
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 ?
Statement $\left( {p \wedge q} \right) \to \left( {p \vee q} \right)$ is