Enter Set Data
Use commas, semicolons, spaces, or line breaks. Duplicates are removed automatically. You can type numbers, letters, words, or symbols.
Example Data Table
| Example Item | Value | Meaning |
|---|---|---|
| Set A | {1, 2, 3, 4} | Base reference set |
| Set B | {3, 4, 5} | Comparison set |
| Set C | {4, 6} | Optional third set |
| Universal Set U | {1, 2, 3, 4, 5, 6, 7} | Universe for complements |
| A ∪ B | {1, 2, 3, 4, 5} | All distinct members from A and B |
| A ∩ B | {3, 4} | Shared members only |
| Aᶜ relative to U | {5, 6, 7} | Everything in U that is not in A |
Formula Used
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 △ B = (A \ B) ∪ (B \ A)
Complement
Aᶜ = U \ A
Cardinality and Product
|A × B| = |A| × |B| and |P(A)| = 2^|A|
How to Use This Calculator
- Enter elements for Set A and Set B. Add Set C if needed.
- Enter the universal set if you want complement results.
- Choose the delimiter style that matches your input.
- Select the output ordering and Cartesian preview limit.
- Enable case sensitivity only when uppercase and lowercase must differ.
- Type one element to test membership across all sets.
- Click Calculate Set Logic to display results above the form.
- Use the CSV or PDF buttons to download the generated results.
Frequently Asked Questions
1. What input format should I use for sets?
You can enter items with commas, semicolons, spaces, or line breaks. The calculator trims spaces and removes duplicates automatically before running every operation.
2. What happens if I leave the universal set empty?
The calculator automatically builds U from the union of A, B, and C. This keeps complement results usable without forcing a separate universal set entry.
3. Does item order matter in set logic?
Mathematically, order does not matter. This page lets you preserve input order or sort results so the displayed output stays convenient for review.
4. Are repeated elements counted more than once?
No. Sets contain unique elements only. Repeated values are removed during parsing, so counts, unions, intersections, and complements remain mathematically correct.
5. Can I mix words, letters, and numbers?
Yes. The calculator accepts symbols, words, labels, letters, and numbers as plain set elements. Each unique token is treated as a single member.
6. What does symmetric difference mean?
Symmetric difference returns items that belong to exactly one of the two sets. Shared elements are excluded, so it highlights differences cleanly.
7. Why might a complement result look incomplete?
Complements are always measured against U. If U does not include every possible element you expect, the complement can only use the members available inside that universe.
8. What does the Cartesian product preview show?
It shows ordered pairs from A × B. The preview limit avoids oversized tables while still helping you inspect pair structure and total product size.