The conditional $(p \wedge q) \Rightarrow p$ is :-

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

If $p, q, r$ are simple propositions with truth values $T, F, T$ respectively, then which of the following is not a true statement?

If the truth value of the compound statement $[(p \leftrightarrow q) \land (q \to r) \land \sim r] \to (p \land \sim q)$ is false, then the truth values of the statement patterns $(p \to q) \leftrightarrow (q \to r)$ and $\sim (p \lor r) \to (q \land p)$ are, respectively ...

Given the statement: "If a quadrilateral is a parallelogram,then its diagonals bisect each other."
Identify the following statements as the contrapositive or converse of the given statement:
$(i)$ If the diagonals of a quadrilateral do not bisect each other,then the quadrilateral is not a parallelogram.
$(ii)$ If the diagonals of a quadrilateral bisect each other,then it is a parallelogram.

The negation of the statement "For all real numbers $x$ and $y, x+y=y+x$" is