Describe any three inference rules

1. Modus Ponens. If you know $P$ and $P\to Q$, you may write down $Q$. In the rules of inference, it's understood that symbols like "$P$" and "$Q$" may be replaced by any statements, including compound statements.

2. Double Negation. In any statement, you may substitute $P$ for  $\neg\neg P$ or  $\neg\neg P$ for $P$ (and write down the new statement).

3. Modus Tollens. If you know $\neg Q$  and $P\to Q$ , you may write down  $\neg P.$