Complement

Definition

The complement of a set A, denoted by A', consists of all elements not in A but within the universal set U. The universal set U contains all possible elements under consideration.

5 Must Know Facts For Your Next Test

1. The complement of a set, A', includes all elements that are in the universal set U but not in A.
2. If an element is in set A, it cannot be in its complement A'.
3. The intersection of a set and its complement is always the empty set.
4. The union of a set and its complement is always the universal set.
5. In Venn diagrams, the shaded area representing the complement of A includes all regions outside circle A within the rectangle representing the universal set.

Review Questions

• What does the complement of a set include?
• What is the result of intersecting a set with its complement?
• How is the complement of a set represented in a Venn diagram?

Related terms

Universal Set: A collection containing all possible elements under consideration.

Intersection: A new set containing all elements common to both sets.

Union: A new set containing all elements from both sets combined.