Build, compare, and visualize finite sets with flexible inputs. Track membership, cardinality, and relations quickly. Solve classroom, homework, and analysis tasks with confidence today.
Use commas, new lines, semicolons, pipes, or spaces. Duplicate values are removed automatically. Case sensitivity can be toggled below.
| Example | Set A | Set B | Set C | Universal Set U | A ∪ B | A ∩ B | A △ B |
|---|---|---|---|---|---|---|---|
| Numeric Sets | {1, 2, 3, 4} | {3, 4, 5, 6} | {4, 6, 8} | {1, 2, 3, 4, 5, 6, 7, 8, 9} | {1, 2, 3, 4, 5, 6} | {3, 4} | {1, 2, 5, 6} |
| Text Sets | {red, blue, green} | {green, yellow, black} | {blue, black} | {red, blue, green, yellow, black, white} | {red, blue, green, yellow, black} | {green} | {red, blue, yellow, black} |
Union: A ∪ B contains every unique element from both sets.
Intersection: A ∩ B contains only common elements.
Difference: A − B contains elements in A but not in B.
Symmetric Difference: A △ B = (A − B) ∪ (B − A).
Complement: Aᶜ = U − A, where U is the universal set.
Cardinality: |A| equals the number of unique elements in A.
Jaccard Similarity: J(A,B) = |A ∩ B| / |A ∪ B|.
Dice Coefficient: D(A,B) = 2|A ∩ B| / (|A| + |B|).
The calculator also reports subset tests, power set size, membership checks, universal set coverage, and Cartesian product size for deeper analysis.
It supports commas, new lines, semicolons, pipes, and spaces. Auto detect works well for most entries. Duplicate elements are removed so each set remains mathematically valid.
No. Sets contain unique elements only. If you enter the same value more than once, the calculator keeps a single copy and ignores the duplicates.
A universal set is required for complements. Without U, the calculator cannot determine which elements should remain outside A, B, or C but still belong to the overall domain.
Union combines all unique elements from both sets. Symmetric difference keeps only elements that appear in exactly one of the sets, excluding the overlap.
Yes. The calculator works with text labels, numbers, or mixed symbols. Each item is treated as a distinct element after trimming extra spaces.
When case sensitivity is enabled, values like Apple and apple are treated as different elements. When disabled, they are considered the same entry.
This page reports Jaccard similarity and Dice coefficient. Both compare overlap against total size, helping you judge how closely related two sets are.
The calculator reports total size for A × B and a preview of ordered pairs. Large products are limited in the preview so the page stays readable.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.