Which concept partitions a set into equivalence classes such that related elements are in the same class?

Which concept partitions a set into equivalence classes such that related elements are in the same class?

• A. Equivalence Relation
• B. Function
• C. Subset
• D. Relation

Answer: (A)

An equivalence relation on a set is a relation that is reflexive, symmetric, and transitive, and it creates a partition of the set into equivalence classes. Each element belongs to exactly one class, and two elements lie in the same class precisely when they are related by the relation. For example, integers grouped by congruence modulo n form classes where members differ by a multiple of n. A general relation or a function or a subset does not necessarily produce such a partition into disjoint, covering classes. So the concept described is an equivalence relation.

An equivalence relation on a set is a relation that is reflexive, symmetric, and transitive, and it creates a partition of the set into equivalence classes. Each element belongs to exactly one class, and two elements lie in the same class precisely when they are related by the relation. For example, integers grouped by congruence modulo n form classes where members differ by a multiple of n. A general relation or a function or a subset does not necessarily produce such a partition into disjoint, covering classes. So the concept described is an equivalence relation.