Negation of $(p \Rightarrow q) \Rightarrow(q \Rightarrow p)$ is
$(\sim p) \vee q$
$(\sim q) \wedge p$
$q \wedge(\sim p )$
$p \vee(\sim q )$
The proposition $ \sim \left( {p\,\vee \sim q} \right) \vee \sim \left( {p\, \vee q} \right)$ is logically equivalent to
$(p\; \wedge \sim q) \wedge (\sim p \wedge q)$ is
Consider the statement : "For an integer $n$, if $n ^{3}-1$ is even, then $n$ is odd." The contrapositive statement of this statement is
Which of the following is equivalent to the Boolean expression $\mathrm{p} \wedge \sim \mathrm{q}$ ?
The false statement in the following is