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

BGM

TS Contributor
#2
\( (B - A) \cup A = (B \cap A^c) \cup A = (B \cup A) \cap (A \cup A^c) = (B \cup A) \cap U = B \cup A \)

where \( U \) is the universe.

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