The expression $ \sim ( \sim p\, \to \,q)$ is logically equivalent to
$ \sim p\, \wedge \sim \,q$
$ p\, \wedge \sim \,q$
$ \sim p\, \wedge \,\,q$
$p\, \wedge \,\,q$
The propositions $(p \Rightarrow \;\sim p) \wedge (\sim p \Rightarrow p)$ is a
If statement $(p \rightarrow q) \rightarrow (q \rightarrow r)$ is false, then truth values of statements $p,q,r$ respectively, can be-
The negation of the statement $(p \vee q)^{\wedge}(q \vee(\sim r))$ is
The negative of $q\; \vee \sim (p \wedge r)$ is
Which of the following is not a statement