Laws of Logical Equivalence

De Morgan's Laws

$\neg (p \wedge q) \equiv \neg p \lor \neg q$

$\neg (p \lor q) \equiv \neg p \wedge \neg q$

$p \wedge T \equiv p$

$p \lor F \equiv p$

$p \lor T \equiv T$

$p \wedge F \equiv F$

$p \lor p \equiv p$

$p \wedge p \equiv p$

$\neg (\neg p) \equiv p$

$p \lor q \equiv q \lor p$

$p \wedge p \equiv q \wedge p$

$(p \lor q) \lor r \equiv p \lor (q \lor r)$

$(p \wedge q) \wedge r \equiv p \wedge (q \wedge r)$

$p \lor (q \wedge r) \equiv (p \lor q) \wedge (p \lor r)$

$p \wedge (q \lor r) \equiv (p \wedge q) \lor (p \wedge r)$

$p \lor (p \wedge q) \equiv p$

$p \wedge (p \lor q) \equiv p$

$p \lor \neg p\equiv T$

$p \wedge \neg p \equiv F$