Podzbiorom

Podzbiorom is the dative plural form of the Polish noun podzbiór, which means subset. In Polish grammar, podzbiór is masculine and its plural forms include podzbiory (nominative), podzbiorów (genitive), podzbiorom (dative), and podzbiorami (instrumental). The form podzbiorom appears when the sentence requires a dative plural noun, for example in phrases that convey “to the subsets” or “for the subsets.” Thus, podzbiorom functions as a grammatical inflection rather than as a separate mathematical concept.

In mathematics, podzbiór (and its inflected forms including podzbiorom) denotes a subset. A subset A of a set B satisfies A ⊆ B, meaning every element of A is also an element of B. If A ⊆ B and A ≠ B, A is a proper subset of B (podzbiór właściwy). The relation ⊆ is a partial order on the power set of a given set, and the concept leads to constructs such as the power set P(X), the set of all subsets of X. Common examples illustrate these ideas: for X = {1, 2, 3}, the set A = {1, 2} is a subset of X, and A is a proper subset of X. The empty set is a subset of every set.

Podzbiorom, as the dative plural form, appears in Polish mathematical prose when referring to multiple subsets in dative context. While the core idea of a podzbiór is universal in set theory, its Polish inflection adapts to the grammatical role it plays in a sentence.