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.
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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?
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.