Calculator Inputs
Example Data Table
| Universe U | Set A | Set B | Set C | Example Output |
|---|---|---|---|---|
| {1, 2, 3, 4, 5, 6, 7, 8} | {1, 2, 3, 4} | {3, 4, 5, 6} | {2, 4, 6, 8} | A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 8} |
| {1, 2, 3, 4, 5, 6, 7, 8} | {1, 2, 3, 4} | {3, 4, 5, 6} | {2, 4, 6, 8} | A ∩ B = {3, 4} |
| {1, 2, 3, 4, 5, 6, 7, 8} | {1, 2, 3, 4} | {3, 4, 5, 6} | {2, 4, 6, 8} | Aᶜ = {5, 6, 7, 8} |
Formula Used
Set theory problems often combine direct element operations with counting rules. This solver supports both methods.
- Union: A ∪ B contains elements in A or B or both.
- Intersection: A ∩ B contains elements common to both sets.
- Difference: A − B contains elements in A but not in B.
- Complement: Aᶜ = U − A, where U is the universe.
- Symmetric difference: A △ B = (A − B) ∪ (B − A).
- Power set cardinality: |P(A)| = 2|A|.
- Cartesian product size: |A × B| = |A| × |B|.
- Inclusion–exclusion: |A ∪ B ∪ C| = |A| + |B| + |C| − |A∩B| − |A∩C| − |B∩C| + |A∩B∩C|.
How to Use This Calculator
- Enter the universe and sets as comma-separated values.
- Choose the operation you want to solve.
- Use the optional count fields when a problem gives region counts instead of elements.
- Press Solve Set Problem to show the result above the form.
- Review the result table, explanation, and chart.
- Use the CSV or PDF buttons to save your output.
FAQs
1. What input format should I use for sets?
Use comma-separated values such as 1,2,3 or apple,banana,orange. Spaces are trimmed automatically, and duplicate entries are removed before solving.
2. Do elements have to be numbers?
No. The solver accepts text labels, numbers, symbols, or mixed entries. It treats each trimmed item as a set element.
3. When should I enter the universe?
Enter the universe when solving complements or when you want outside-region counts. For union or intersection alone, the universe is optional.
4. Why are duplicates removed?
Sets contain unique elements by definition. Repeated entries do not change membership, so the solver keeps only one copy of each value.
5. Why is the power set limited?
Power sets grow extremely fast. A set with 10 elements already has 1,024 subsets, so the display is limited to keep the page practical.
6. What does the inclusion–exclusion mode do?
It solves problems where you know counts like |A|, |B|, |A∩B|, and |A∩B∩C|, but not the full element lists.
7. Can I export the solution?
Yes. Use the CSV button for spreadsheet-friendly output and the PDF button for a printable report of the current result section.
8. Why do I see negative Venn regions?
Negative regions usually mean the count inputs are inconsistent. Recheck intersection totals, triple overlap, and the universe size before drawing conclusions.