# how to prove the set conculsion:(B-A)U A=B (if A is subset of B)?

#### luofeiyu

##### New Member
how to prove the set conculsionB-A)U A=B (if A is subset of B)?

#### BGM

##### TS Contributor
$$(B - A) \cup A = (B \cap A^c) \cup A = (B \cup A) \cap (A \cup A^c) = (B \cup A) \cap U = B \cup A$$

where $$U$$ is the universe.

When $$A \subseteq B$$, then $$B \cup A = B$$ and hence the result follows.