Union and Intersection Calculator
Calculate union, intersection, and set differences with step-by-step explanations
Set Operations Calculator
Set A
Set B
Example Problems
Example 1: Sports Activities
Amy's activities: 5 (jogging, cycling, dancing, swimming, basketball)
Mark's activities: 2 (dancing, tennis, soccer, cycling)
Union: Activities at least one of them likes
Intersection: Activities both of them like
Example 2: Number Intervals
Interval A: [1, 10] (numbers from 1 to 10, inclusive)
Interval B: (5, 15) (numbers from 5 to 15, exclusive)
Union: All numbers covered by either interval
Intersection: Numbers covered by both intervals
Example 3: Three Sets of Colors
Primary: red, blue, yellow
Secondary: green, orange, purple
Warm: red, orange, yellow
Demonstrates: Complex three-set relationships
Set Theory Symbols
Union
Elements in at least one set
Intersection
Elements in all sets
Empty Set
Set with no elements
Set Notation
Elements enclosed in braces
Set Theory Tips
Union is always larger than or equal to intersection
Operations are commutative: A∪B = B∪A
Empty set is subset of every set
Use Venn diagrams to visualize relationships
Understanding Union and Intersection of Sets
What are Sets?
A set is a well-defined collection of distinct objects, called elements or members. Sets can contain numbers, letters, words, or any other objects. The order of elements doesn't matter, and each element appears only once.
Union (A ∪ B)
- •Contains all elements that belong to at least one of the sets
- •Always a superset of both original sets
- •Size equals |A| + |B| - |A ∩ B|
Intersection (A ∩ B)
- •Contains only elements that belong to all sets
- •Always a subset of both original sets
- •Can be empty if sets have no common elements
Properties
Commutative: A ∪ B = B ∪ A
Associative: (A ∪ B) ∪ C = A ∪ (B ∪ C)
Distributive: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)