# subset

(definition)

**Definition:**
A *set* S_{1} is a subset of another set S_{2} if every element in S_{1} is in S_{2}. S_{2} may have exactly the same elements as S_{1}.

**Formal Definition:** S_{1} ⊆ S_{2} iff ∀ s, s ∈ S_{1} → s ∈ S_{2}.

**Specialization** (... is a kind of me.)

*proper subset*, *combination*.

**See also**
*superset*.

*Note:
If S*_{1} is a subset of S_{2}, S_{2} is a superset of S_{1}.

* A combination is a subset with exactly n elements.*

Author: PR

## Implementation

generating subsets (Fortran, Mathematica, and Pascal)

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Dictionary of Algorithms and Data
Structures home page.

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with Paul Black.

Entry modified 2 March 2015.

HTML page formatted Wed Mar 13 12:42:46 2019.

Cite this as:

Patrick Rodgers, "subset", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 2 March 2015. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/subset.html