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Union, Intersection, and Symmetric Difference Calculator — result sheet
Calculate the union, intersection, directional differences, symmetric difference, and cardinality relationship of two finite sets.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A ∪ B contains either set; A ∩ B contains shared elements; A △ B = (A\B) ∪ (B\A); |A ∪ B| = |A| + |B| − |A ∩ B|.
The page presents the core two-set operations together so visitors can connect the listed members to the cardinality identity. Set differences and the symmetric difference make it clear which elements belong only to one side.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Set A elements — Comma- or semicolon-separated tokens; duplicates are ignored.
- Set B elements — Comma- or semicolon-separated tokens; duplicates are ignored.
Worked example
| Input | Value |
|---|---|
| Set A elements | 1, 2, 3, 4 |
| Set B elements | 3, 4, 5, 6 |
A∪B = {1, 2, 3, 4, 5, 6}, A∩B = {3, 4}, A△B = {1, 2, 5, 6}, and |A∪B| = 6.
Assumptions and limits
- Elements are compared as exact trimmed text tokens, so capitalization and spelling are significant.
- The input represents finite sets with at most 100 distinct tokens per side.
- Repeated tokens do not increase cardinality and are listed once in each output set.
- No universal set is assumed, so a complement is not calculated.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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