Calculator Inputs
Use commas, semicolons, or new lines between elements. Supported operators include union, intersection, difference, symmetric difference, complement, and parentheses.
Example Data Table
| U | A | B | C | Expression | Result |
|---|---|---|---|---|---|
| {1, 2, 3, 4, 5, 6, 7, 8} | {1, 2, 3, 4} | {3, 4, 5} | {2, 5, 6} | (A ∩ B) Δ C | {3, 4, 2, 5, 6} |
| {a, b, c, d, e} | {a, b, c} | {b, d} | {c, e} | (A ∪ B) - C | {a, b, d} |
| {10, 20, 30, 40, 50} | {10, 30, 50} | {20, 30, 40} | {10, 20} | (A' ∩ B) ∪ C | {20, 40, 10} |
Formula Used
This evaluator follows standard set algebra and applies operators from the innermost parentheses outward, while respecting complement, difference, intersection, symmetric difference, and union precedence.
- Union:
A ∪ B = {x | x ∈ A or x ∈ B} - Intersection:
A ∩ B = {x | x ∈ A and x ∈ B} - Difference:
A - B = {x | x ∈ A and x ∉ B} - Symmetric difference:
A Δ B = (A - B) ∪ (B - A) - Complement:
A' = U - A - Cardinality:
|A|equals the number of unique elements in set A.
How to Use This Calculator
- Enter the universal set U when you plan to use complements.
- Fill sets A through F using comma-separated, semicolon-separated, or line-separated elements.
- Type an expression with supported operators such as
∪,∩,-,Δ, and'. - Press Evaluate Expression to see the result above the form, including element lists, sizes, and the graph.
- Use the CSV and PDF buttons to export the evaluation summary for reports, teaching notes, or review files.
Frequently Asked Questions
1. Which operators does this evaluator support?
It supports union, intersection, difference, symmetric difference, complement, and parentheses. You can write symbols such as ∪ and ∩ or text forms like UNION, INTERSECTION, and XOR.
2. How is complement calculated?
Complement is always computed against the universal set U. For example, A' means every element in U that does not appear in A.
3. Are duplicate values allowed in input sets?
You may enter duplicates, but the evaluator removes repeats automatically. Sets always behave as collections of unique elements.
4. Can I use text values instead of numbers?
Yes. Elements can be numbers, words, codes, or labels. The tool treats each trimmed item as a distinct symbol.
5. What happens when spaces appear in inputs?
Extra spaces around elements are trimmed automatically. Spaces inside an element name remain part of that element if you do not split it with commas, semicolons, or line breaks.
6. What if a set includes elements outside U?
The expression still evaluates, but the tool flags a note. Complements only use U, so values outside U are not added into a complement result.
7. How is symmetric difference different from union?
Union keeps everything from both sets. Symmetric difference keeps only elements that belong to exactly one of the two sets.
8. What do the CSV and PDF downloads include?
They export the evaluated expression, all entered sets, the result set, its cardinality, and whether the result is a subset of U.