网站需求怎么做,谷歌网站,手机网站主页设计,消防有哪些网站合适做离散数学和组合数学什么关系关系类型 (Types of Relation) There are many types of relation which is exist between the sets, 集合之间存在许多类型的关系#xff0c; 1. Universal Relation 1.普遍关系 A relation r from set a to B is said to be universal if: R A…离散数学和组合数学什么关系 关系类型 (Types of Relation) There are many types of relation which is exist between the sets, 集合之间存在许多类型的关系 1. Universal Relation 1.普遍关系 A relation r from set a to B is said to be universal if: R A * B 从组a到b关系R被认为是通用的如果R A * B Example: 例 A {1,2} B {a, b} A {1,2} B {ab} R { (1, a), (1, b), (2, a), (2, b) is a universal relation. R {(1a)(1b)(2a)(2b)是普遍关系。 2. Compliment Relation 2.称赞关系 Compliment of a relation will contain all the pairs where pair do not belong to relation but belongs to Cartesian product. 关系的称赞将包含所有对其中对不属于关系而是属于笛卡尔积。 R A * B – X R A * B – X Example: 例 A { 1, 2} B { 3, 4}
R { (1, 3) (2, 4) }
Then the complement of R
Rc { (1, 4) (2, 3) }
3. Empty Relation 3.空关系 A null set phie is subset of A * B. 空集phie是A * B的子集。 R phie is empty relation R phi是空关系 4. Inverse of relation 4.关系逆 An inverse of a relation is denoted by R^-1 which is the same set of pairs just written in different or reverse order. Let R be any relation from A to B. The inverse of R denoted by R^-1 is the relation from B to A defined by: 关系的逆由R ^ -1表示 R ^ -1是只是以不同或相反顺序写入的同一对对的集合。 令R为从A到B的任何关系。 R的逆表示由R ^ -1是从B到A的关系由下式定义 R^-1 { (y, x) : yEB, xEA, (x, y) E R}
5. Composite Relation 5.复合关系 Let A, B, and C be any three sets. Let consider a relation R from A to B and another relation from B to C. The composition relation of the two relation R and S be a Relation from the set A to the set C, and is denoted by RoS and is defined as follows: 令A B和C为任意三个集合。 让我们考虑从A到B的关系R和从B到C的另一个关系。 两个关系R和S的组成关系是从集合A到集合C的一个关系用RoS表示并定义如下 Ros { (a, c) : an element of B such that (a, b) E R and (b, c) E s, when a E A , c E C}Hence, (a, b) E R (b, c) E S (a, c) E RoS. Ros {(ac)B的元素当EAc EC时具有(ab)ER和(bc)E s 因此(ab)ER(bc)ES (ac)E RoS 。 6. Equivalence Relation 6.等价关系 The relation R is called equivalence relation when it satisfies three properties if it is reflexive, symmetric, and transitive in a set x. If R is an equivalence relation in a set X then D(R) the domain of R is X itself. Therefore, R will be called a relation on X. 关系R如果满足集合x中的自反对称和可传递的三个属性则称为等价关系。 如果R是集合X中的等价关系则D(R)的R域是X本身。 因此 R将被称为X上的关系。 The following are some examples of the equivalence relation: 以下是等价关系的一些示例 Equality of numbers on a set of real numbers. 一组实数上的数字相等。 Equality of subsets of a universal set. 通用集的子集的相等性。 Similarities of triangles on the set of triangles. 三角形集上三角形的相似性。 Relation of lines being a parallel onset of lines in a plane. 线的关系是平面中线的平行起点。 Relation of living in the same town on the set of persons living in Canada. 在加拿大居住的同一套城镇中居住的关系。 7. Partial order relation 7.偏序关系 Let, R be a relation in a set A then, R is called partial order Relation if, 假设R是集合A中的一个关系那么如果R被称为偏序关系 R is reflexive R是反身的 i.e. aRa ,a belongs to A 即aRaa属于A R is anti- symmetric R是反对称的 i.e. aRb, bRa a b, a, b belongs to a 即aRbbRa a bab属于a R is transitive R是可传递的 aRb, bRc aRc, a, b, c belongs to A aRbbRc aRcabc属于A 8. Antisymmetric Relation 8.反对称关系 A relation R on a set a is called on antisymmetric relation if for x, y if for x, y 如果对于xy则对集合a的关系R称为反对称关系对于xy If (x, y) and (y, x) E R then x y 如果(xy)和(yx)ER则x y Example: { (1, 2) (2, 3), (2, 2) } is antisymmetric relation. 示例{(12)(23)(22)}是反对称关系。 A relation that is antisymmetric is not the same as not symmetric. A relation can be antisymmetric and symmetric at the same time. 反对称关系与非对称关系不相同。 一个关系可以同时是反对称的和对称的。 9. Irreflective relation 9.反射关系 A relation R is said to be on irreflective relation if x E a (x ,x) does not belong to R. 关系R被说成是对irreflective关系如果x E中的(XX)不属于R上 。 Example: 例 a {1, 2, 3}
R { (1, 2), (1, 3) if is an irreflexive relation
10. Not Reflective relation 10.非反思关系 A relation R is said to be not reflective if neither R is reflexive nor irreflexive. 如果R既不是自反的也不是自反的则关系R被认为是不反射的。 翻译自: https://www.includehelp.com/basics/types-of-relation-discrete mathematics.aspx离散数学和组合数学什么关系
