What is the symmetric difference of two sets?

The symmetric difference (A △ B) is the set of elements that are in exactly one of the two sets — present in A or B but not in both. It equals (A − B) ∪ (B − A).

Are duplicate elements counted?

No. A set contains each element at most once, so duplicates inside a single input are removed automatically before any operation runs.

Is my data uploaded anywhere?

No — every operation runs locally in your browser and nothing is sent to a server.

What is the difference between union and intersection?

The union (A ∪ B) gathers every element found in either set, while the intersection (A ∩ B) keeps only the elements shared by both. Union is usually larger; intersection is usually smaller.

Is A − B the same as B − A?

No. A − B keeps elements that are in A but not B, while B − A keeps elements in B but not A. They are generally different sets, which is why the tool offers both.

Does the order of elements matter?

No. Sets are unordered, so {1, 2, 3} and {3, 1, 2} are the same set. Only which elements are present matters, and duplicates within an input are ignored.

Set Operations Calculator

Set operations calculator

Compute the core operations of set theory on two sets: union (A ∪ B), intersection (A ∩ B), difference (A − B and B − A), and symmetric difference (A △ B). It is for maths students, data wranglers and anyone comparing two lists of values.

How it works

Each input is split on commas and new lines, trimmed, and deduplicated — a set holds each member at most once. The chosen operation then runs:

Operation	Result
Union (A ∪ B)	every element in A or B
Intersection (A ∩ B)	elements in both A and B
Difference (A − B)	elements in A but not B
Difference (B − A)	elements in B but not A
Symmetric difference (A △ B)	elements in exactly one set

The symmetric difference equals (A − B) ∪ (B − A). The result and its cardinality (the number of members) are shown.

Example

With A = 5 and B = 7:

Operation	Result	Size
Union	7	7
Intersection	5	2
A − B	3	3
Symmetric difference	7	5

Pick an operation and the result updates instantly — all in your browser, with no network calls.