Math & Algebra Tool
Set Theory Calculator
Union, Intersection, and Difference of sets.
Input Sets
Frequently Asked Questions
What is a Set?+
A set is a well-defined collection of distinct objects, considered as an object in its own right. The objects are called elements or members of the set.
What is the Union (A ∪ B)?+
The Union of two sets A and B contains all elements that are in A, OR in B, OR in both. It combines the members of both sets.
What is the Intersection (A ∩ B)?+
The Intersection contains only the elements that are present in BOTH set A AND set B. It finds the common ground between sets.
What is the Difference (A - B)?+
The Difference (or relative complement) contains elements that are in set A but NOT in set B. It essentially 'subtracts' any B members from A.
What is the empty set (∅)?+
The empty set (or null set) is the unique set having no elements. Its size or cardinality is zero. It is a subset of every set.
Are duplicates allowed in a set?+
No. By definition, sets contain unique elements. {1, 2, 2, 3} is treated exactly the same as {1, 2, 3}.