Which of the following logical statements is a tautology?

Solution

1. A tautology is a statement that is true for all possible truth values of its components.
2. For $p\vee \neg p$, if $p$ is true, $\neg p$ is false, so $T\vee F=T$.
3. If $p$ is false, $\neg p$ is true, so $F\vee T=T$.
4. Since the result is always true, it is a tautology.
5. Hence the answer is (C).