| either φ or ψ φ ∨ ψ ≃ ¬ (¬ φ ∧ ¬ ψ) at least 1 true—not both false | ▿ | not both φ and ψ ¬ (φ ∧ ψ) ≃ ¬ φ ∨ ¬ ψ not both true—at least 1 false | 
| ⫫ | ⋈ | ⫫ | 
| both φ and ψ φ ∧ ψ ≃ ¬ (¬ φ ∨ ¬ ψ) both true—neither false | ▵ | neither φ nor ψ ¬ (φ ∨ ψ) ≃ ¬ φ ∧ ¬ ψ neither true—both false |