Prove That A − (A ∩ B) = A − B

Solution

\[ A-(A\cap B) \] \[ =A\cap(A\cap B)’ \] \[ =A\cap(A’\cup B’) \] \[ =(A\cap A’)\cup(A\cap B’) \] \[ =\phi\cup(A\cap B’) \] \[ =A\cap B’ \] \[ =A-B \]

Hence proved.