A ∪( B∪C)=(A∪B)∪( A∪C)

(A∪B)∩C =(A∪C)∩( B∪C)

Turn left x∈

Namely x∈A∪B and x ∈ c.

Namely (x∈A or x∈B) and x ∈ c.

Taking the first formula as an example, the left formula =p∧x≤p, and at the same time p≥p and p∨q≥p, so it can be proved that the left formula ≥ right formula.

Law of absorption

(P ∨ 0) ∧ (P ∨ Q) = P ∨ (0 ∧ Q) = P ∨ 0 = P

(P∧ 1)∨( P∧Q)= P ∧( 1∨Q)= P∧ 1 = P

The = sign here should be understood as the logical equivalence in the formula.

The law of absorption does not apply to coherent logic, linear logic and substructure logic. In the case of substructure logic, there is no one-to-one correspondence between free variables of identity definition pairs.