Calculator Inputs
Enter comma-separated elements. The solver treats values as case-sensitive labels.
Example Data Table
Use these samples to test different set relations and solution counts.
| Universe U | A | B | C | Equation | Example Solution |
|---|---|---|---|---|---|
| {1, 2, 3, 4, 5, 6} | {1, 2} | {1, 2, 4} | {1, 3, 4, 6} | X ∪ A = B | X = {4} |
| {a, b, c, d} | {a, b, c} | {a, c} | {b, d} | X ∩ A = B | X may be {a, c} or {a, c, d} |
| {2, 4, 6, 8} | {2, 8} | {4, 6} | ∅ | X Δ A = B | X = {2, 4, 6, 8} |
| {p, q, r, s} | {p} | {r, s} | {p, r, s} | (X ∪ A) ∩ C = B | No solution |
Formula Used
The calculator solves the unknown set X by evaluating the chosen equation against every subset of the universe U.
- Union: X ∪ A contains elements in X or A.
- Intersection: X ∩ A contains elements shared by X and A.
- Difference: X \ A contains elements in X but not in A.
- Reverse difference: A \ X contains elements in A but not in X.
- Symmetric difference: X Δ A = (X \ A) ∪ (A \ X).
- Complement: Xᶜ = U \ X.
- Search space: total candidate sets = 2|U|.
- Solution rule: keep each candidate X where f(X, A, C, U) = B.
How to Use This Calculator
- Enter the universe U as comma-separated elements such as 1, 2, 3, 4.
- Enter set A and target set B. Add set C only when the selected equation uses it.
- Select the equation form that matches your problem statement.
- Press Solve Set Equation to compute all valid sets X.
- Review the status, quick checks, and full solution table shown above the form.
- Use the CSV or PDF buttons to export the current result or example table.
Frequently Asked Questions
1. What kind of equations can this solver handle?
It handles ten forms involving union, intersection, difference, complement, symmetric difference, and mixed equations with an optional constraint set C.
2. Why does the universe matter?
Every complement and every candidate solution is defined relative to U. Changing U can change both the number of candidates and the final solutions.
3. Why are there sometimes many solutions?
Some equations leave certain elements unrestricted. In those cases, several subsets of U satisfy the same target set B.
4. Why does the solver limit the universe size?
The solver checks every subset of U. That means 12 elements already create 4,096 candidates, so larger universes slow the page noticeably.
5. Are duplicate elements allowed in input fields?
Duplicates are removed automatically. The calculator keeps only unique values and orders sets according to the universe you entered.
6. Can I use letters instead of numbers?
Yes. Elements are treated as text labels, so numbers, letters, and short words all work as long as they belong to U.
7. What does “No solution” mean?
It means no subset of U makes the selected left-hand expression exactly equal the target set B under your current inputs.
8. What do the export buttons save?
The result export saves the solved summary and solution table. The example export saves the sample table for reference or teaching notes.