Axioms of Boolean algebras

¬¬A = A,
A ∨ B = B ∨ A,  A ∧ B = B ∧ A,
(A ∨ B) ∨ C = A ∨ (B ∨ C),  (A ∧ B) ∧ C = A ∧ (B ∧ C),
A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C),  A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C),
A ∨ A = A,  A ∧ A = A,
A ∨ (A ∧ B) = A,  A ∧ (A ∨ B) = A,
A ∨ 1 = 1,  A ∧ 0 = 0,
A ∨ 0 = A,  A ∧ 1 = A,
¬A ∨ A = 1,  ¬A ∧ A = 0,
¬(A ∨ B) = ¬A ∧ ¬B,  ¬(A ∧ B) = ¬A ∨ ¬B.

Axioms of MV-algebras

A ∨^{L} B = B ∨^{L} A,
(A ∨^{L} B) ∨^{L} C = A ∨^{L} (B ∨^{L} C),
A ∨^{L} 0 = A,
¬¬A = A,
¬0 = 1,
A ∨^{L} 1 = 1,
¬(¬A ∨^{L} B) ∨^{L} B = ¬(¬B ∨^{L} A) ∨^{L} A.

Lattice operations in MV-algebras

A ∨ B = ¬(¬A ∨^{L} B) ∨^{L} B  A ∧ B = ¬(¬A ∧_{L} B) ∧_{L} B

Distributivity laws in MV-algebras

A ∨ (B ∧ C) = (A ∨ B) ∧ (A ∨ C)  A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C)
A ∨^{L} (B ∧ C) = (A ∨^{L} B) ∧ (A ∨^{L} C)  A ∧_{L} (B ∨ C) = (A ∧_{L} B) ∨ (A ∧_{L} C)
A ∨^{L} (B ∨ C) = (A ∨^{L} B) ∨ (A ∨^{L} C)  A ∧_{L} (B ∧ C) = (A ∧_{L} B) ∧ (A ∧_{L} C)