Discrete Mathematics (13): Closure of relations, equivalence relations, partial order relations

1. Closure 

1) Definition

2) Construct a closure based on the relationship matrix

3) Construct a closure based on the relationship graph

2. Equivalence relationship

To study the equivalence relation is to divide the set A according to the relation R on the set A (purpose).

1) Equivalence relationship:

Let R be a relation on a non-empty set . If R is reflexive, symmetric and transitive , then R is called an equivalence relation on A. Let R be an equivalence relation if < x , y >∈ R , say that x is equivalent to y , and denote it as x ~ y . 

2) Equivalence class : 

 

 3) Shops

4) Division of collections

 

3. Partial order relationship