The Laws of Logic

Discrete Mathematics

Law of Double Negation

De Morgan’s Laws

Commutative Laws

P V Q is logical equivalence to Q V P
P A Q is logicsl equivalnece to Q A P

Associative Laws

P V (Q V R) is logical equivalence to (P V Q) V R
P A (Q A R) is logical equivalence to (P A Q) A R

Distributive Laws

P V (Q A R) is logical equivalence to (P V Q) A (P V R)

P A (Q V R) is logical equivalence to (P A Q) V (P A R)

Idempotent Laws

P V P is logical equivalence to P

P A P is logical equivalence to P

Identity Laws

P V F0 is logical equivalence to P

P A T0 is logical equivalence to P

Inverse Laws

P V not P is logical equivalence to T0

P A not P is logical equivalence to F0

Domination Laws

P V T0 is logical equivalence to T0

P A F0 is logical equivalence to F0

Absorption Laws

P V (P A Q) is logical equivalence to P

P A (P V Q) is logical equivalence to P

Contradiction

F0

Always False

Tautology

T0

Always True