Which of the following is not logically equivalent to the proposition : “A real number is either rational or irrational”.
If a number is neither rational nor irrational then it is not real
If a number is not a rational or not an irrational, then it is not real
If a number is not real, then it is neither rational nor irrational
If a number is real, then it is rational or irrational
$(p \wedge \, \sim q)\, \wedge \,( \sim p \vee q)$ is :-
The contrapositive of the statement "If I reach the station in time, then I will catch the train" is
The statement $[(p \wedge q) \rightarrow p] \rightarrow (q \wedge \sim q)$ is
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 negation of the Boolean expression $ \sim \,s\, \vee \,\left( { \sim \,r\, \wedge \,s} \right)$ is equivalent to