Wednesday 27 June 2012

How to Define Binary Relation

In the previous post we have discussed about Use Percentage Increase Calculator

and In today's session we are going to discuss about A binary relation R is said to be defined in set A if for any order pair(x,y)ϵ A x A , it is meaningful to say

That xRy   is true or false. In other words R= (x,y) ϵ A x A : xRy   is true

That is relation R in a set A is a subset of A x A. The meaning of binary is two. So binary relation is a relation between two sets, these sets may be different or identical. For the sake of convenience a binary relation will be written as only as relation. In other terms we can say dyadic relation and two place relation are called synonyms of binary relations. (Know more about Binary Relation in broad manner, here,)

Binary relation concepts are used in many branches of mathematics like ‘is greater than’, ‘is equal to ’and divides are used in arithmetic’s and ‘is congruent to ’ is used in geometry and ‘is adjacent to’ used in graph theory. Like that more concepts are used in different -2 branches. The binary relation is also used in other relation like Domain relation .For example Domain D of the relation R is defined as the set of all first element of the ordered pairs which belongs to R

Like binary relation D = x :(x,y) ϵ R , x ϵ A

Range E of the relation R is defined as the set of all first element of the ordered pairs which belongs to R

E  = y :(x,y) ϵ R , x ϵ B

As well as binary relation is also used in computer science filed.

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