🔄 Set Theory Explorer
Interactive learning tool for understanding sets, unions, intersections, and more!
Interactive Venn Diagram
Set Operations
Practice Problems
Quick Reference
Interactive Venn Diagram
Set A:
Set B:
Universal Set U:
Select Operation:
Show Sets
A ∪ B
A ∩ B
A - B
A'
B'
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Result:
Click "Show Sets" to begin
Set Operations Calculator
Set A:
Set B:
Universal Set (for complements):
Union (A ∪ B)
Intersection (A ∩ B)
Difference (A - B)
Symmetric Difference (A ⊕ B)
Complement of A (A')
Complement of B (B')
Results:
Practice Problems
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Set Theory Quick Reference
Basic Notation
Set:
A collection of distinct objects
Element:
An object in a set (∈)
Empty Set:
∅ or { }
Universal Set:
U (contains all elements being considered)
Subset:
A ⊆ B (every element of A is in B)
Set Operations
Union:
A ∪ B (all elements in A or B)
Intersection:
A ∩ B (elements in both A and B)
Difference:
A - B (elements in A but not B)
Complement:
A' (elements in U but not A)
Symmetric Difference:
A ⊕ B (elements in A or B, but not both)
Set Laws
Commutative:
A ∪ B = B ∪ A
Associative:
(A ∪ B) ∪ C = A ∪ (B ∪ C)
Distributive:
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
De Morgan's:
(A ∪ B)' = A' ∩ B'
Identity:
A ∪ ∅ = A, A ∩ U = A
Venn Diagram Guide
Circle A:
Represents set A
Circle B:
Represents set B
Overlap:
Shows intersection A ∩ B
Outside circles:
Elements not in A or B
Rectangle:
Universal set U
Examples
Example 1:
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}
A ∪ B = {1, 2, 3, 4, 5, 6}
A ∩ B = {3, 4}
A - B = {1, 2}
B - A = {5, 6}