Subsets [list]
gives a list of all possible subsets of list.
Subsets [list,n]
gives all subsets containing at most n elements.
Subsets [list,{n}]
gives all subsets containing exactly n elements.
Subsets [list,{nmin,nmax}]
gives all subsets containing between nmin and nmax elements.
Subsets [list,nspec,s]
limits the result to the first s subsets.
Subsets [list,nspec,{s}]
gives if possible the s^(th) subset.
Subsets
Subsets [list]
gives a list of all possible subsets of list.
Subsets [list,n]
gives all subsets containing at most n elements.
Subsets [list,{n}]
gives all subsets containing exactly n elements.
Subsets [list,{nmin,nmax}]
gives all subsets containing between nmin and nmax elements.
Subsets [list,nspec,s]
limits the result to the first s subsets.
Subsets [list,nspec,{s}]
gives if possible the s^(th) subset.
Details
- Subsets [list] gives the power set of list.
- Subsets [list] orders subsets with shortest first, and later elements in list omitted first.
- If the elements of list are in the order returned by Sort , then the complete result from Subsets [list] will also be in this order.
- Subsets [list,All ] is equivalent to Subsets [list].
- Subsets [list,{nmin,nmax,dn}] gives subsets containing nmin, nmin+dn, … elements.
- Subsets [list,nspec,spec] gives the same result as Take [Subsets[list,nspec],spec], provided that the elements specified by spec are present.
Examples
open all close allBasic Examples (2)
All possible subsets (power set):
All possible subsets containing up to 2 elements:
Subsets containing exactly 2 elements:
Scope (4)
The first 5 subsets containing 3 elements:
All subsets with even length:
The 69381^(st) subset:
All subsets of {a,b,c,d}:
The odd-numbered subsets of {a,b,c,d} in reverse order:
Generalizations & Extensions (1)
Use any head:
Applications (7)
Find all ways to pick 3 elements from 4:
Draw lines between all pairs of points in an octagon:
Construct an elementary symmetric polynomial:
All possible subsets of the divisors of 10:
Find integers that have exactly 3 nonzero binary digits:
Join all possible pairs of 20 random points in 3D:
Draw lines between all pairs of points in a cube:
Properties & Relations (3)
Possible Issues (1)
Neat Examples (2)
Polygons formed from all possible triples of random points:
Tech Notes
History
Introduced in 2004 (5.1)
Text
Wolfram Research (2004), Subsets, Wolfram Language function, https://reference.wolfram.com/language/ref/Subsets.html.
CMS
Wolfram Language. 2004. "Subsets." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Subsets.html.
APA
Wolfram Language. (2004). Subsets. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Subsets.html
BibTeX
@misc{reference.wolfram_2025_subsets, author="Wolfram Research", title="{Subsets}", year="2004", howpublished="\url{https://reference.wolfram.com/language/ref/Subsets.html}", note=[Accessed: 05-December-2025]}
BibLaTeX
@online{reference.wolfram_2025_subsets, organization={Wolfram Research}, title={Subsets}, year={2004}, url={https://reference.wolfram.com/language/ref/Subsets.html}, note=[Accessed: 05-December-2025]}