Question

prove that (A') = (A' U B)

Answer 1

A-B = set of elements which are in A but not in B = A - (AnB)
B-A = set of elements which are in B but not in A = B - (AnB).
Therefore, (A-B) U (B-A) = (AUB) - (AnB)
By drawing Venn Diagram, this can be established.

Answer 2

this is true only if there is no intersection between sets A and B
(AB) = empty set
then B would completely be in A' making it equal to the union of A' and B

Answer 3

In terms of a Venn diagram,

When A and B are disjoint (i.e. \(A\cap B=\emptyset \), then \(A'=A'\cup B\)