To visualize relationships between 2, 3 or 4 sets we quite often use
pictures called Venn diagrams. The standard way to draw these diagrams
for 1, 2 and 3 sets is illustrated here. The enclosing rectangle
represents the universe.
Observe that the Venn diagram with n sets partitions the universe into pieces.
Here is a picture of the 4 set Venn diagram.