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

L luofeiyu New Member Oct 3, 2013 #1 Oct 3, 2013 #1 how to prove the set conculsionB-A)U A=B (if A is subset of B)?

BGM TS Contributor Oct 3, 2013 #2 Oct 3, 2013 #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.

\( (B - A) \cup A = (B \cap A^c) \cup A = (B \cup A) \cap (A \cup A^c) = (B \cup A) \cap U = B \cup A \) where \( U \) is the universe. When \( A \subseteq B \), then \( B \cup A = B \) and hence the result follows.