The dual of $\left(x^{\prime} \vee y^{\prime}\right) = x \wedge y$ is

Give three examples of sentences which are not statements. Give reasons for the answers.

Consider
Statement-$1$: $(p \wedge \sim q) \wedge (\sim p \wedge q)$ is a fallacy.
Statement-$2$: $(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$ is a tautology.

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?

In a Boolean Algebra $B$,for all $x, y \in B$,$x \wedge (x \vee y)$ is equal to

The Boolean expression $\sim(p \vee q) \vee (\sim p \wedge q)$ is equivalent to: