This advanced subset calculator helps you generate subsets, estimate power set sizes, compare two sets, test subset relationships, and review key operations with downloadable output.
Subset Calculator
Subset Size Visualization
Example Data Table
| Input Set A | Input Set B | Subset Size Filter | Union Size | Intersection Size |
|---|---|---|---|---|
| 1, 2, 3 | 2, 3, 4 | 2 | 4 | 2 |
| a, b, c, d | b, d | all | 4 | 2 |
| red, blue | blue, green | 1 | 3 | 1 |
Formula Used
Total subsets of a set: If a set has n elements, the number of subsets is 2n.
Subsets with exactly r elements: C(n, r) = n! / (r! × (n-r)!).
Subset test: Set A is a subset of Set B when every element of A appears in B.
Proper subset: A is a proper subset of B when A ⊆ B and A ≠ B.
Set operations: Union combines unique elements, intersection keeps common elements, and differences keep exclusive elements.
How to Use This Calculator
- Enter values for Set A using commas, semicolons, or new lines.
- Add Set B if you want subset checks and set comparisons.
- Select a subset size filter or leave it on all sizes.
- Choose how many generated subsets should appear in the table.
- Press Calculate Subsets to show the results above the form.
- Review summary cards, subset listings, and the Plotly chart.
- Use the CSV and PDF buttons to export your results.
FAQs
1. What is a subset?
A subset is a set containing only elements from another set. Every element in the smaller set must also exist in the original set.
2. What is a power set?
A power set is the collection of all possible subsets of a set. It includes the empty set and the full original set.
3. Why does a set with n elements have 2^n subsets?
Each element has two choices: included or excluded. Multiplying those choices across n elements gives 2^n total combinations.
4. What is the empty set?
The empty set has no elements. It is a valid subset of every set and is usually written as ∅.
5. What is a proper subset?
A proper subset contains only elements from another set, but it is not identical to that larger set. It must be strictly smaller.
6. Why are duplicate values removed?
Sets contain unique elements by definition. Removing duplicates keeps the input mathematically correct and prevents misleading subset counts.
7. Why are only some subsets displayed?
Large sets produce huge power sets quickly. The display limit keeps the page fast, readable, and easier to export.
8. Can this calculator compare two sets too?
Yes. It can test subset relationships and compute union, intersection, differences, and symmetric difference using your two entered sets.