Részhalmazrelációval

Részhalmazrelációval, also known as subset relation, is a fundamental concept in set theory, a branch of mathematical logic. It refers to the relationship between two sets where all elements of one set are also elements of the other set. If set A is a subset of set B, it is denoted as A ⊆ B. This relation is reflexive, meaning every set is a subset of itself, and transitive, meaning if A is a subset of B and B is a subset of C, then A is a subset of C. The subset relation is also antisymmetric, meaning if A is a subset of B and B is a subset of A, then A and B are equal sets.

The subset relation is distinct from the proper subset relation, denoted as A ⊊ B, which implies that A is a subset of B but A is not equal to B. In other words, A ⊊ B means that B contains at least one element that is not in A.

The subset relation is widely used in various areas of mathematics and computer science, including graph theory, where it is used to define the concept of a subgraph, and in database theory, where it is used to define the concept of a relational database schema. It is also a key concept in the study of formal languages and automata theory, where it is used to define the concept of a language accepted by a finite automaton.