Exercise 1 For each of the following logical expressions, say whether they are tautologies, or give counterexamples. Assume that the domain of quantification ("For all what? There exists a what?") is the Boolean values TRUE and FALSE, so "Vp" means "for all Boolean values p." (a) Vp.Vq. pVqp@q (b) Vp.Vq. pqpVq

Given that the domain of quantification is the Boolean values TRUE and FALSE.

A logical statement is said to be Tautology, if it is True for all possibilities.

Given that $p$ and $q$ are two statements.

We know that the compound statement $p\vee q$ is true if at least one of $p$ or $q$ is true, it is false when both $p$ and $q$ are false.

We know that the compound statement $p\oplus q$ is true if exactly one of the $p$ or $q$ is true and otherwise false.

We know that the truth table of $p\Rightarrow q$ can be written as: