Type your sets and this free set calculator works out the union, intersection, differences, symmetric difference and complements, checks subsets, lists the power set and Cartesian product, and draws a Venn diagram for two or three sets. Great for set theory homework and discrete maths.
Set operations explained
| Operation | Symbol | Meaning | A = {1,2,3,4,5}, B = {4,5,6,7} |
|---|---|---|---|
| Union | A ∪ B | in A or B (or both) | {1,2,3,4,5,6,7} |
| Intersection | A ∩ B | in both A and B | {4,5} |
| Difference | A − B | in A but not B | {1,2,3} |
| Symmetric difference | A Δ B | in exactly one of them | {1,2,3,6,7} |
| Complement | A′ | in U but not A | {6,7,8,9,10} for U = 1–10 |
Sets ignore order and repeats, so {3, 1, 1, 2} is the same set as {1, 2, 3}. Elements can be numbers, letters or words, and matching is case-sensitive.
Frequently asked questions
How do I find the union and intersection of two sets?
The union A ∪ B contains every element that is in A, in B or in both. The intersection A ∩ B contains only the elements they share. Enter both sets, separated by commas, and the calculator lists both with their sizes.
How do I find the complement of a set?
The complement A′ is every element of the universal set U that is not in A. Enter U (for example 1-10) and the calculator lists A′, B′ and the complement of their union and intersection.
What is the symmetric difference?
A Δ B is the set of elements in exactly one of the two sets, i.e. (A − B) ∪ (B − A). It is like an “exclusive or” for sets.
Can it draw a Venn diagram with three sets?
Yes. Fill in Set C and the diagram switches to three overlapping circles, with every region’s elements and counts.
What is a power set?
The power set P(A) is the set of all subsets of A, including the empty set and A itself. A set with n elements has 2ⁿ subsets, so the calculator lists them in full for sets of up to 6 elements.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.