A compound sentence is a $\textit{tautology}$ if it is true independently of the truth values of its component atomic sentences. A sentence is $\textit{atomic}$ if it contains no sentential connectives.
A sentence $P$ is said to $\textit{tautologically imply}$ a sentence $Q$ if and only if the conditional $P \rightarrow Q$ is a tautology.
When two sentences tautologically imply each other, they are said to be $\textit{tautologically equivalent.}$ P and Q are tautologically equivalent when and only when the biconditional $P \leftrightarrow Q$ is a tautology.
If $P$ and $Q$ are distinct atomic sentences, the sentence $P$ tautologically equivalent to which of the following? (More than one option may be correct)
- $\neg P \rightarrow P$
- $P \rightarrow \neg P$
- $P \vee Q$
- $P \vee \neg P$