Elementary Logic

Detour: Some Laws for Calculational Proofs
Equivalence is commutative and associative
A ↔ B ≡ B ↔ A
A ↔ (B ↔ C) ≡ (A ↔ B) ↔ C
⊥ ∨ A ≡ A ∨ ⊥ ≡ A
¬A ∧ A ≡ ⊥
A → B ≡ ¬A ∨ B
A → ⊥ ≡ ¬A
(A ∨ B) → C ≡ (A → C) ∧ (B → C)
A → (B → C) ≡ (A ∧ B) → C
A → B ≡ A ↔ (A ∧ B)
A ∧ B ⇒ A
Yih-Kuen Tsay (SVVRL @ IM.NTU) Elementary Logic FLOLAC 2011 27 / 64