[이산수학3-4]Equivalence Relations(동치관계)

동치 관계 - relation R이 reflexive, symmetric, and transitive on a set X이면 X는 "동치 관계 on X"라고 불린다. Theorem1 ▷ 분할(partition)은 relation으로 정의될 수 있다.

Let S be a partition of a set X. Define xRy to mean that for some set s in S, both x and y belong to s.

Then R is reflexive, symmetric, and transitive. Theorem2 Let R be an equivalence relation on a set X.

For each a ∈ X, let [a] = {x ∈ X | xRa}. (In words, [a] is the set of all elements in X that are related to a.)

Then S = {[a] | a ∈ X} is a partition o...