Below is a standard Logical Equivalences Table used in propositional logic and discrete mathematics. It shows common pairs of logically equivalent expressions.
| Name of Law | Logical Equivalence |
|---|---|
| Identity Laws | ( p \land T \equiv p ) ( p \lor F \equiv p ) |
| Domination Laws | ( p \lor T \equiv T ) ( p \land F \equiv F ) |
| Idempotent Laws | ( p \lor p \equiv p ) ( p \land p \equiv p ) |
| Double Negation Law | ( \neg(\neg p) \equiv p ) |
| Commutative Laws | ( p \lor q \equiv q \lor p ) ( p \land q \equiv q \land p ) |
| Associative Laws | ( (p \lor q) \lor r \equiv p \lor (q \lor r) ) ( (p \land q) \land r \equiv p \land (q \land r) ) |
| Distributive Laws | ( p \lor (q \land r) \equiv (p \lor q) \land (p \lor r) ) ( p \land (q \lor r) \equiv (p \land q) \lor (p \land r) ) |
| De Morgan’s Laws | ( \neg(p \land q) \equiv \neg p \lor \neg q ) ( \neg(p \lor q) \equiv \neg p \land \neg q ) |
| Absorption Laws | ( p \lor (p \land q) \equiv p ) ( p \land (p \lor q) \equiv p ) |
| Negation Laws | ( p \lor \neg p \equiv T ) ( p \land \neg p \equiv F ) |
| Implication Law | ( p \rightarrow q \equiv \neg p \lor q ) |
| Biconditional Law | ( p \leftrightarrow q \equiv (p \rightarrow q) \land (q \rightarrow p) ) |
| Contrapositive Law | ( p \rightarrow q \equiv \neg q \rightarrow \neg p ) |