Let A, B and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C.

Question

Show that B = C.

Answer 1

you can easily prove oit with a Venn diagram.
If not: A�¾B=A+B-A�¿B=A+B-A�¿C
AUC=A+C-A�¿C
As AUB=AUC then A+B-A�¿C=A+C-A�¿C hence; B=C