The logical expression $[p \wedge (q \vee r)] \vee [(\sim p \wedge q) \vee (\sim p \wedge r)]$ is equivalent to

Write the negation of the following statement:
$q:$ There exists a rational number $x$ such that $x^{2} = 2$.

Which of the following is not a correct statement?

Let $\Delta \in \{\wedge, \vee, \Rightarrow, \Leftrightarrow\}$ be such that $(p \wedge q) \Delta ((p \vee q) \Rightarrow q)$ is a tautology. Then $\Delta$ is equal to

For the circuit shown below,the Boolean polynomial is

The statements $p, q$ and $r$ have truth values True, False and False respectively. The truth values of a logical statement $[\sim (p \land \sim q) \lor (q \lor \sim r)]$ and its dual are, respectively.....