subconjunto

Subconjunto is the term used in Spanish and Portuguese for the mathematical concept of subset. A subconjunto A of a set B is a set in which every element of A is also an element of B. This relation is written A ⊆ B and read “A is a subset of B.” If, in addition, A ≠ B, then A is a proper subset of B, sometimes written A ⊂ B or A ⊊ B.

Notationally, A ⊆ B holds exactly when for every element x, if x is in A then x is in B. Subset relations are reflexive (every set is a subset of itself), antisymmetric, and transitive: if A ⊆ B and B ⊆ C, then A ⊆ C.

Key examples help clarify the idea. Let A = {1, 2, 3} and B = {1, 2, 3, 4, 5}. Then A ⊆ B, and A ≠ B, so A is a proper subset of B. The empty set, ∅, is a subset of every set, and every set is a subset of itself (A ⊆ A).

Subsets are central to many constructions. The power set P(S) is the set of all subsets of S. Subset relations interact with set operations: if A ⊆ B, then A ∪ C ⊆ B ∪ C and A ∩ C ⊆ B ∩ C. Subset concepts appear across logic, probability, combinatorics, and computer science.