Are the following pairs of statements negations of each other:
$1$. The number $x$ is a rational number.
$2$. The number $x$ is an irrational number.

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 ...

Write the component statements of the following compound statement and check whether the compound statement is true or false.
"All living things have two legs and two eyes."

Write the following statement in five different ways,conveying the same meaning.
$p:$ If a triangle is equiangular,then it is an obtuse-angled triangle.

Which of the following is an open statement?

If ${(p \wedge \sim q) \wedge (p \wedge r)} \rightarrow (\sim p \vee q)$ has a truth value of $False$,then the truth values of the statements $p, q, r$ are respectively: