The universal set U is the set containing all the elements you are currently considering.

Example 1

If you were working with sets of colors, the universal set would be the set containing all possible colors. If you were working with sets of planets, the universal set would be the set containing all the planets.

Does it seem logical to say that for any set A in the universal set, A ⊆ U? The answer is YES!

Venn Diagrams

We need some way to discuss sets without listing all the elements in order to show certain relationships between the sets. Venn diagrams have one or more circle/s that represent set/s inside a rectangle, where the rectangle represents the universal set.

Figure 1 shows a universal set containing two sets: A, and B. The overlapping of sets A and B indicates the possibility that some elements are common to both of these sets. These common elements would be found in the overlap area.

Figure 1. Venn Diagram Text Alternative

The Venn diagram shows 2 intersecting circles within a rectangle, one labeled A and the other labeled B. The whole area inside the reectangle (in and outside of the circles) is the universal set, labled U.