Subsetrelation
The subset relation, denoted ⊆, is a relation between sets that states A ⊆ B if and only if every element of A is also an element of B. If A ⊆ B but A ≠ B, A is called a proper subset of B and is sometimes written A ⊊ B.
In set theory, the subset relation is a partial order on the class of all sets (and,
The structure (P(U), ⊆), where P(U) is the set of all subsets of U, forms a complete lattice.
Examples: If A = {1, 2} and B = {1, 2, 3}, then A ⊆ B. If A = {1} and
Applications of the subset relation include expressing inclusion hierarchies, defining monotone functions, reasoning about intersections and