Universal set

Definition

The universal set is the set that contains all objects or elements under consideration, typically denoted by the symbol U. It serves as the reference set in Venn diagrams and includes every element of the sets being discussed.

5 Must Know Facts For Your Next Test

1. The universal set includes all possible elements for a particular discussion or problem.
2. In a Venn diagram, the universal set is represented by a rectangle encompassing all other sets.
3. Elements not in any specific subset are still part of the universal set.
4. Any subset within a Venn diagram is contained within the universal set.
5. The complement of a set A (denoted as A') consists of all elements in the universal set that are not in A.

Review Questions

• What symbol is commonly used to denote the universal set?
• How is the universal set represented in a Venn diagram?
• What does it mean if an element is in the complement of a subset?

Related terms

Subset:

A set whose elements are all contained within another set.

Complement:

The set of all elements in the universal set that are not in a given subset.

Intersection:

A new set containing all elements that are common to two or more sets.