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