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.

Write the negation of the following statement:
$r:$ For every real number $x$,either $x > 1$ or $x < 1.$

Rewrite the following statement in the form "$p$ if and only if $q$":
$p:$ If you watch television,then your mind is free and if your mind is free,then you watch television.

Consider the following two statements :
$P :$ If $7$ is an odd number,then $7$ is divisible by $2.$
$Q :$ If $7$ is a prime number,then $7$ is an odd number.
If $V_1$ is the truth value of the contrapositive of $P$ and $V_2$ is the truth value of the contrapositive of $Q,$ then the ordered pair $(V_1, V_2)$ equals

Consider the following statements:
$r: \text{If } p \to q \text{ is false, then } p \lor q \text{ is false.}$
$s: \text{If } p \leftrightarrow q \text{ is false, then } p \lor q \text{ is false.}$
The truth values of $r \to s$ and $s \to r$ are respectively:

In a switching circuit, if the combination $(S_1 \land S_2)$ is connected in parallel to the combination $(S'_1 \land S'_2)$, then the room is lit only when ...