Calculator Form
Single-page layout with a responsive 3-column, 2-column, and 1-column calculator grid.
Example Data Table
| Example | Set A | Set B | Expected Result |
|---|---|---|---|
| Numbers | {1, 2, 3} | {1, 2, 3, 4} | A is a proper subset of B |
| Equal Sets | {a, b, c} | {c, b, a} | Equal sets, not a proper subset |
| Mixed Relation | {red, blue} | {red, green, blue, black} | A is a proper subset of B |
| No Subset | {x, y, z} | {x, y, q} | Neither set is a subset of the other |
Formula Used
A proper subset requires complete inclusion and strict difference.
A ⊂ B ⇔ (∀x, x ∈ A → x ∈ B) and (∃y, y ∈ B and y ∉ A)
For finite deduplicated sets, the checker uses this equivalent rule:
A ⊂ B ⇔ A ⊆ B and |A| < |B|
In practical terms, the calculator removes duplicates, normalizes values using your selected options, checks whether every unique element in Set A appears in Set B, and then confirms that Set B still has at least one additional unique element.
How to Use This Calculator
- Enter elements for Set A and Set B in the two text areas.
- Select the delimiter that separates your elements.
- Turn options on or off for trimming, case sensitivity, numeric normalization, and empty values.
- Click Check Proper Subset to calculate the relationship.
- Read the result summary above the form, then review counts, unique items, and differences.
- Use the CSV or PDF buttons to export your results.
Frequently Asked Questions
1. What is a proper subset?
A proper subset means every element of Set A exists in Set B, and Set B has at least one additional unique element. Equal sets are not proper subsets.
2. Are duplicates counted in the result?
No. Sets use unique elements only, so repeated values are removed before comparison. Raw entry counts still help explain why unique counts may be smaller.
3. Does element order matter?
No. Set comparison ignores order, so values entered in different positions still represent the same mathematical set after normalization.
4. What does case sensitive comparison do?
Case sensitive mode treats uppercase and lowercase text as different values. Turning it off compares text after lowercase normalization.
5. What does numeric normalization do?
Numeric normalization treats values like 01, 1, and 1.0 as the same number when possible, reducing false mismatches in numeric lists.
6. Can the empty set be a proper subset?
Yes. The empty set is a proper subset of every non-empty set, but it is not a proper subset of another empty set.
7. Why do equal sets fail the strict check?
Equal sets fail because proper subsets require strict inclusion. The larger set must contain at least one unique element not found in the smaller set.
8. Which delimiters can I use?
You can split values by commas, semicolons, pipes, tabs, spaces, new lines, or a custom delimiter that you provide.