either φ or ψ
φ ∨ ψ¬ (¬ φ ∧ ¬ ψ)
at least 1 truenot both false
not both φ and ψ
¬ (φ ∧ ψ)¬ φ ∨ ¬ ψ
not both trueat least 1 false
both φ and ψ
φ ∧ ψ¬ (¬ φ ∨ ¬ ψ)
both trueneither false
neither φ nor ψ
¬ (φ ∨ ψ)¬ φ ∧ ¬ ψ
neither trueboth false