Cardinality of the union of two sets
Definition
The cardinality of the union of two sets is the number of unique elements present in both sets combined. It is calculated by adding the cardinalities of each set and subtracting the cardinality of their intersection.
5 Must Know Facts For Your Next Test
- The formula for finding the cardinality of the union of two sets A and B is |A ∪ B| = |A| + |B| - |A ∩ B|.
- The intersection set, denoted as A ∩ B, contains elements that are in both sets A and B.
- If two sets have no elements in common (disjoint), then |A ∩ B| = 0.
- The union set, denoted as A ∪ B, includes every element from both sets without duplication.
- Understanding Venn diagrams can help visually represent and solve problems involving the union and intersection of sets.
Review Questions
- What is the formula to calculate the cardinality of the union of two sets?
- How do you determine if two sets are disjoint when calculating their union's cardinality?
- Explain why it is necessary to subtract the cardinality of the intersection when finding the cardinality of a union.
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Related terms
Cardinality: The number of elements in a set.
Intersection: The set containing all elements that are common to both given sets.
Union: The set containing all distinct elements from both given sets combined.
