Calculator Form
Use commas, semicolons, line breaks, or vertical bars as separators. Curly braces are optional. Example: {1,2,3} or apple, banana, cherry.
Example Data Table
| Example | Set A | Set B | Set C | Universal Set U | Sample Output |
|---|---|---|---|---|---|
| Numeric | {1, 2, 3, 4} | {3, 4, 5} | {2, 4, 6} | {1, 2, 3, 4, 5, 6, 7} | A ∪ B = {1, 2, 3, 4, 5}, A ∩ B = {3, 4}, Aᶜ = {5, 6, 7} |
| Text | {red, blue, green} | {blue, yellow} | {green, black} | {red, blue, green, yellow, black, white} | A △ B = {red, green, yellow}, B \ A = {yellow} |
| Mixed labels | {A1, B2, C3} | {B2, D4} | ∅ | {A1, B2, C3, D4, E5} | A × B has 6 ordered pairs, A ⊆ B = No |
Formula Used
A ∪ B = { x | x ∈ A or x ∈ B } A ∩ B = { x | x ∈ A and x ∈ B } A \ B = { x | x ∈ A and x ∉ B } A △ B = (A \ B) ∪ (B \ A) Aᶜ = U \ A A × B = { (a, b) | a ∈ A and b ∈ B } |A| = number of distinct elements in A P(A) = set of all subsets of AThis calculator treats every entry as a distinct finite-set element. Duplicates are removed during normalization. Complements are computed only relative to the universal set U. Ordered pairs in Cartesian products preserve element order, so (a, b) differs from (b, a).
How to Use This Calculator
- Enter Set A and Set B using commas, semicolons, line breaks, or vertical bars.
- Add Set C if you want three-set unions and intersections.
- Enter Universal Set U if you want complements.
- Optionally type one element to test membership in each set.
- Choose case sensitivity, sorting, and power-set generation options.
- Set the Cartesian preview limit for ordered-pair display.
- Click the calculate button to show results under the header.
- Use the CSV or PDF buttons to export the current result block.
Frequently Asked Questions
1. What separators can I use for elements?
You can separate elements with commas, semicolons, line breaks, or vertical bars. Curly braces are optional. The calculator trims extra spaces automatically before computing each set operation.
2. Why are duplicate values removed?
A mathematical set contains unique elements only. If you enter repeated values, the calculator normalizes the input and keeps one copy of each distinct element.
3. When does complement become available?
Complement needs a universal set U. Without U, the calculator cannot determine which outside elements belong to the complement of A, B, or C.
4. Does element order matter in sets?
No. Sets are unordered collections. The sorting option only changes display order for readability. It does not change the mathematics of union, intersection, difference, or subset relations.
5. What is symmetric difference?
Symmetric difference includes elements that belong to exactly one of the two sets. It excludes elements shared by both sets. Algebraically, it equals (A \ B) ∪ (B \ A).
6. Can I use words instead of numbers?
Yes. The calculator works with numeric values, words, labels, and mixed identifiers. When case sensitivity is enabled, Red and red are treated as different elements.
7. Why is the power set sometimes skipped?
Power sets grow very quickly. A set with n elements has 2^n subsets. To keep output practical, this page skips power-set generation when a set has more than eight elements.
8. Why is the Cartesian product preview limited?
Large sets can produce thousands of ordered pairs. The calculator shows the full count, but only previews a limited number of pairs so the result section stays readable and exportable.