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.
Worked example
With A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}:
| Operation | Result | Size |
|---|---|---|
| Union | {1, 2, 3, 4, 5, 6, 7} | 7 |
| Intersection | {4, 5} | 2 |
| A − B | {1, 2, 3} | 3 |
| B − A | {6, 7} | 2 |
| Symmetric difference | {1, 2, 3, 6, 7} | 5 |
Pick an operation and the result updates instantly — all in your browser, with no network calls.
Practical data-wrangling uses
Set operations on lists of values come up constantly in data work, even when the problem is not framed in mathematical terms.
Finding new customers: you have last month’s customer IDs in Set A and this
month’s in Set B. B − A gives you new customers who appeared this month. A − B
gives you churned customers who did not return.
Deduplicating two lists: import two exports from different systems and take the union. The result is a merged, deduplicated list with each entry exactly once.
Finding common records: you have a list of users who completed step 1 (A) and a list who completed step 2 (B). The intersection gives you users who completed both — your conversion funnel’s pass-through rate.
Spotting discrepancies: you expect two systems to hold the same user IDs. The symmetric difference shows you the IDs that appear in exactly one system — these are the mismatches to investigate.
Set theory notation quick reference
- A ∪ B (union): in A or B (or both)
- A ∩ B (intersection): in A and B
- A − B (difference): in A but not B; also written A \ B
- A △ B (symmetric difference): in A or B but not both; A △ B = (A ∪ B) − (A ∩ B)
- |A| (cardinality): the number of elements in set A
- A set contains each element at most once; order does not matter