47. Sia: A = {2, 3, 4, 5, 6, 7, 8}; B = {13, 15, 16, 17, 20, 26, 27, 30}; C = {3, 5, 7, 8}; D = {15, 17, 26, 30}. Provare che risulta: (A ∪ B) − (C ∪ D) = (A − C) ∪ (B − D).

A − C = {2, 4, 6} e B − D = {13, 16, 20, 27}. Quindi (A − C) ∪ (B − D) = {2, 4, 6, 13, 16, 20, 27}.

D’altra parte, C ∪ D = {3, 5, 7, 8, 15, 17, 26, 30}. Eliminando questi elementi da A ∪ B si ottiene (A ∪ B) − (C ∪ D) = {2, 4, 6, 13, 16, 20, 27}.

I due membri sono uguali.