How does the Set Theory Calculator work?

Union A∪B: all elements in A or B (or both) Then: Intersection A∩B: elements in both A and B Then: Difference A−B: elements in A but not B Then: Symmetric difference A△B: in A or B but not both.

Can you give an example of how to use the Set Theory Calculator?

Example: Input A={1,2,3,4,5}, B={3,4,5,6,7} gives a result of A∪B={1,2,3,4,5,6,7}, A∩B={3,4,5}, A−B={1,2}.

Is the Set Theory Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Set Theory Calculator?

Our Set Theory Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Set Theory Calculator

Set A (space/comma separated)

Set B

Set theory is the mathematical study of collections of distinct objects. Operations like union (∪), intersection (∩), and difference (−) describe how sets relate to each other and underlie all of modern mathematics and computer science.

Symbol	Name	Unit	Description
∪	Union	—	All elements in either set
∩	Intersection	—	Elements in both sets
−	Difference	—	Elements in first set but not second

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Pro Tip

Venn diagrams are the visual form of set operations — the overlapping region is the intersection.

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Did You Know?

The entire number system (natural, integer, rational, real) is built on set theory axioms developed by Georg Cantor in the 1870s.

References

›Stanford Encyclopedia of Philosophy — Set Theory

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Set Theory Calculator

Set Theory Calculator

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Set Theory Calculator