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
The number of choices of $\Delta \in\{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$, such that $( p \Delta q ) \Rightarrow(( p \Delta \sim q ) \vee((\sim p ) \Delta q ))$ is a tautology, is
Which of the following is equivalent to the Boolean expression $\mathrm{p} \wedge \sim \mathrm{q}$ ?
Statement $-1$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is equivalent to $p \leftrightarrow q$
Statement $-2$ : $ \sim \left( {p \leftrightarrow \, \sim q} \right)$ is a tautology.
The Boolean expression $\left(\sim\left(p^{\wedge} q\right)\right) \vee q$ is equivalent to
Which one of the following Boolean expressions is a tautology?