Which of the following is a contradiction
$(p \wedge q) \wedge \sim (p \vee q)$
$p \vee (\sim p \wedge q)$
$(p \Rightarrow q) \Rightarrow p$
None of these
Which of the following is the negation of the statement "for all $M\,>\,0$, there exists $x \in S$ such that $\mathrm{x} \geq \mathrm{M}^{\prime \prime} ?$
The inverse of the proposition $(p\; \wedge \sim q) \Rightarrow r$ is
Which of the following is not logically equivalent to the proposition : “A real number is either rational or irrational”.
Which of the following statement is true
If the Boolean expression $\left( {p \oplus q} \right) \wedge \left( { \sim p\,\Theta\, q} \right)$ is equivalent to $p \wedge q$, where $ \oplus $ , $\Theta \in \left\{ { \wedge , \vee } \right\}$ , ,then the ordered pair $\left( { \oplus ,\Theta } \right)$ is