Disjunction ∨
Disjunction, also known as a logical OR, is a basic operation in propositional logic. The statment φ ∨ ψ
is true, if either φ is true, ψ is true, or both are true.
Truth Table

(<> (\/ (T) (T)) (T)) /edit/peano_new/prop.gh/orTT

(<> (\/ (T) (F)) (T)) /edit/peano_new/prop.gh/orTF

(<> (\/ (F) (T)) (T)) /edit/peano_new/prop.gh/orFT

(<> (\/ (F) (F)) (F)) /edit/peano_new/prop.gh/orFF
Definition
Disjunction is defined using the conditional and negation: (<> (\/ ph ps) (> (. ph) ps)) /edit/peano_new/prop.gh/dfor
Properties

Commutation: (<> (\/ ph ps) (\/ ps ph)) /edit/peano_new/prop.gh/orcom

Association: (<> (\/ (\/ ph ps) ch) (\/ ph (\/ ps ch))) /edit/peano_new/prop.gh/orass

Idempotence: (<> (\/ ph ph) ph) /edit/peano_new/prop.gh/oridm

Distribution: (<> (\/ ph (/\ ps ch)) (/\ (\/ ph ps) (\/ ph ch))) /edit/peano_new/prop.gh/ordi

De Morgan's Law: (<> (\/ ph ps) (. (/\ (. ph) (. ps)))) /edit/peano_new/prop.gh/oran
Propositional Logic