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This tool handles two common subset questions: is one set fully contained within another, and how many (and which) subsets of a specific size exist within a set?
How it works
For a subset check, every element of set A is verified against set B — if all are found, A ⊆ B. For listing size-k subsets, every combination of k elements is enumerated directly, matching the "n choose k" count from the combinations formula.
- Enter what do you want to do?.
- Enter set A (comma-separated, for subset check).
- Enter set B (comma-separated, for subset check).
- Enter set (comma-separated, for size-k subsets).
- Enter subset size (k).
- Click Calculate to see your results.
Examples
A subset check
{1,2} is a subset of {1,2,3,4} since both 1 and 2 are found in the larger set.
Listing size-2 subsets
The size-2 subsets of {a,b,c} are {a,b}, {a,c}, and {b,c} — 3 in total, matching "3 choose 2" = 3.
Who should use it
- Set theory and discrete mathematics coursework.
- Combinatorics problems requiring specific subset enumeration.
Industry applications
- Computer science and discrete mathematics education
Advantages
- Handles both the subset-check and size-k-enumeration use cases in one tool.
- Explicitly reports which elements are missing when a subset check fails.
Limitations
- Size-k enumeration is capped at a 10-element set to keep the subset list readable.
Common mistakes to avoid
- Confusing "subset" with "proper subset" — every set is a subset of itself, but not a proper subset of itself.
Best practices
- When checking A ⊆ B by hand, go through every element of A one at a time rather than trying to compare the sets as a whole.
Tips
- The Power Set Calculator on this site lists every subset of every size at once — use it instead if you need the complete power set rather than just one fixed size.