Prove That A ∪ (B − A) = A ∪ B
Question:
Show that for any sets \( A \) and \( B \),
\[ A\cup(B-A)=A\cup B \]Solution
\[ A\cup(B-A) \] \[ =A\cup(B\cap A’) \] \[ =(A\cup B)\cap(A\cup A’) \] \[ =(A\cup B)\cap U \] \[ =A\cup B \]Hence proved.
Question:
Show that for any sets \( A \) and \( B \),
\[ A\cup(B-A)=A\cup B \]Hence proved.