(i) A set of pencils and a set of pens have a null set as intersection.
(ii) A set of points in a plane, cardinal directions: N S E W. This has 4 subsets: points north, points south, points east, points west. Something similar is the points in the x-y plane (divided into quadrants). The subsets are quadrant 1, all points where x and y are positive (including zero); quadrant 2, where x is negative and y is positive; quadrant 3 where both x and y are negative; quadrant 4, where x is positive and y is negative.