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

Simplify the following switching circuit and find the corresponding Boolean expression.

Write the following statement in the form "if $p$,then $q$":
$q$: There is a traffic jam whenever it rains.

Consider the following statements:
$p$: If voltage increases, then current decreases.
$q$: If voltage does not increase, then current does not decrease.
$r$: If current decreases, then voltage increases.
$s$: If current does not decrease, then voltage does not increase.
Which of the following pairs of statements have the same meaning?

The symbolic form of the following circuit is (where $p$ and $q$ represent switches $S_{1}$ and $S_{2}$ being closed respectively):

The minimum number of switches in the simplified form of the following switching circuit is