Calculator Form
Plotly Graph
The chart compares the main set counts and highlights the size of the symmetric difference.
Example Data Table
| Example | Set A | Set B | Symmetric Difference | Count |
|---|---|---|---|---|
| Numbers | {1, 2, 3, 4, 8} | {3, 4, 5, 6, 8, 10} | {1, 2, 5, 6, 10} | 5 |
| Letters | {a, b, c, d} | {c, d, e, f} | {a, b, e, f} | 4 |
| Words | {cat, dog, fish} | {dog, bird, fish, lion} | {cat, bird, lion} | 3 |
Formula Used
The symmetric difference contains elements that belong to exactly one of the two sets.
Here, A \ B means elements found only in A, B \ A means elements found only in B, and A ∩ B means the common elements shared by both sets.
How to Use This Calculator
- Enter the elements for Set A and Set B.
- Select the input delimiter that matches your data.
- Choose number mode or text mode.
- Enable case-sensitive matching only when needed.
- Pick an output style and sort order.
- Click the calculate button to generate the result.
- Review the exclusive elements, intersection, union, and chart.
- Use the CSV or PDF buttons to export the result summary.
FAQs
1. What is symmetric difference in set theory?
It is the set of elements that appear in exactly one of the two sets. Shared elements are removed, while exclusive elements from both sets remain in the final answer.
2. How is symmetric difference different from union?
Union includes every distinct element from both sets. Symmetric difference excludes elements found in both sets and keeps only the non-overlapping values.
3. Does order matter in a set?
No. Sets are unordered collections, so the calculator removes repeated entries and works with unique elements. Sorting is only for display convenience.
4. Can I use words instead of numbers?
Yes. Choose text mode to compare words, labels, or symbols. You can also turn case sensitivity on when uppercase and lowercase should be treated differently.
5. What happens when both sets are identical?
The symmetric difference becomes the empty set because every element appears in both sets, leaving no exclusive values behind.
6. Can this calculator handle custom delimiters?
Yes. Select custom delimiter and enter the symbol or text you use, such as a pipe, slash, or another separator.
7. Why does the calculator ignore duplicates?
Set theory treats each element as unique. Repeated entries do not change membership, so the calculator normalizes them into a proper set before computing results.
8. What does the cardinality formula show?
It shows the number of elements in the symmetric difference. The formula subtracts twice the shared count because common values must be removed from both set totals.