Set Theory Calculator

All math tools

Perform operations like Union, Intersection, and Difference on two sets.

Input Sets

Set A (comma separated)

Set B (comma separated)

Set Operations

{ 1, 2, 3, 4, 5, 6 }

Union (A ∪ B)

Relationships and commonalities between member sets.

Cardinality |A|4

Cardinality |B|4

Intersection (A ∩ B)

{ 3, 4 }

Difference (A - B)

{ 1, 2 }

Difference (B - A)

{ 5, 6 }

Symmetric Difference (A Δ B)

{ 1, 2, 5, 6 }

About this calculator

What is Set Theory?

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Modern set theory is the foundation of much of mathematics, providing a language for describing functions, numbers, and structures.

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Pro Tips

Sets do not care about order: {1, 2} is the same as {2, 1}.
Duplicate elements are automatically removed in most set operations.
The empty set (∅) is a subset of every set.

Fun Facts

"Giorgi Cantor, the father of set theory, proved that some infinities are larger than others."
"The 'Universal Set' contains all objects under consideration in a particular context."
"Venn diagrams were introduced by John Venn in 1880 to visually represent set relationships."

Formula: A ∪ B = {x : x ∈ A or x ∈ B}