Wir gehen Schritt für Schritt vor:

A ∪ (B ∩ C ) = {x |x ∈ A ∨ x ∈ B ∩ C } Def.Vereinigung = {x |x ∈ A ∨ (x ∈ B ∧ x ∈ C )} Def.Schnitt = {x |(x ∈ A ∨ x ∈ B ) ∧ (x ∈ A ∨ x ∈ C )} Distributivgesetz“ ” = {x |x ∈ A ∪ B ∧ x ∈ A ∪ C } Def.Vereinigung = (A ∪ B ) ∩ (A ∪ C) Def.Schnitt