Let set B=A' the complement of A. Let A and B be represented by two circles. A\B=A<intersection>B, but B has no elements in common with A by definition of B, except the null set Ø. Therefore A<intersection>B=Ø=A\A.
In the circles, the A circle contains all the elements of A while the B circle contains none of them. Both circles contain Ø, the null or empty set. So the intersection of A and B circles contains only the empty set.