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Subset and Set Difference Calculator — result sheet
Check whether one finite set is a subset or proper subset of another and list the elements missing from either direction.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A ⊆ B when every element of A is in B; A ⊂ B when A ⊆ B and A ≠ B; A\B contains elements in A but not B.
The calculator treats each comma- or semicolon-separated token as one finite-set element, removes repeated entries, and reports both directional differences. This makes the inclusion decision auditable instead of hiding it inside a single yes/no answer.
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 |
| Set B elements | 1, 2, 3, 4 |
A is a proper subset of B; A\B is empty, B\A is {4}, |A| = 3, and |B| = 4.
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 because a set records membership rather than multiplicity.
- This tool does not parse algebraic expressions, intervals, fuzzy values, or infinite set notation.
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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