Laws of Logic
Double Negation
\(\neg \neg p \iff p\)
Disjunctive Syllogism
\((p \lor q) \land \neg p \implies q\)
Modus Ponens
\((p \rightarrow q) \land p \implies q\)
Modus Tollens
\((p \rightarrow q) \land (\neg q) \implies \neg p\)
Law of Contrapositive
\((p \rightarrow q) \iff (\neg q \rightarrow \neg p)\)
De Morgan's Laws
\(\neg(p \land q) \iff (\neg p \lor \neg q)\)
\(\neg(p \lor q) \iff (\neg p \land \neg q)\)
Distributive Laws
\((p \land (q \lor r)) \iff (p \land q)\lor(p \land r)\)
\((p \lor (q \land r)) \iff (p \lor q)\land(p \lor r)\)