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
- The complement of a set, A', includes all elements that are in the universal set U but not in A.
- If an element is in set A, it cannot be in its complement A'.
- The intersection of a set and its complement is always the empty set.
- The union of a set and its complement is always the universal set.
- 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?
"Complement" appears in:
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.
