Properties of Ordered Pairs

Analytical geometry was invented by Rene Descartes and Pierre de Fermat in the 16th century and the cartesian plane was designed. It is heavily used in the field of computing and programming language 

Ordered Pair is a part of the Coordinate System which deals with the location of a point in an accurate manner. Ordered Pair is typically used to locate a point in the Coordinate System. In Order Pair, we have a pair of numbers, the first of which is called the abscissa and the second of which is called the ordinate.

Ordered Pair (3, 4) does not equal Ordered Pair (4, 3). Thus, Order in a Pair is significant, and an Ordered Pair consists of two items expressed in a certain order.

It won’t be satisfactory if we talk about the definition of ordered pairs. It is only based on a descriptive and impulsive understanding of order. 

What Are Set Relation and Function 

Sets, relations, and functions 3  are all interconnected topics. Sets denote the gathering of ordered components whereas relations and functions outline the operations performed on sets. The relations outline the affiliation between the 2 given sets

In arithmetic, a relation is any assortment of ordered pairs. The very fact that the pairs are ordered is very important and implies that the ordered pair (a, b) is different from the ordered pair (b, a) unless a = b. For most relations, the elements of the ordered pairs are naturally associated or connected in one way or another.

What is Ordered Pair

An ordered pair consists of two elements in each order. For example, if A and B are any 2 sets then by an ordered pair of elements, we mean a pair(a, b) in that order where a ϵ A and b ϵ B.

Ordered pair examples:-

Let us take some examples of the set, (1, 2) (2, -3) (-5, -3) i.e., A pair of numbers arranged in a specific order is known as ordered pair 

• Equality of ordered pairs 

Two ordered pairs  (a1, b1)  and (a2, b2) are equal if and only if a1=a2 and  b1=b2

• Cartesian product sets 

Let us take two sets,  A and B be any two non-empty sets. The set of all ordered pairs(x, y) such that xϵA and yϵB are called the cartesian product of the sets. And is denoted by A X B. Thus, we have

A x B = {(x, y): x ϵ A and y ϵ B}

Let us take an example if R be the set of all real numbers, then

RxR = {(x, y): x ϵ R, y ϵ R}, i.e., R x R is the set of all points in the cartesian plane. It is also denoted by R²

Since relations are sets at ordered pairs, they could be graphed on the ordinary coordinate plane only if they have ordered pairs of real numbers as their elements. 

Ordered Pairs in given Universal relation:-

So for (a, a), a total number of ordered pairs = n and a total number of relations = 2n. if neither (a,b) nor (b,a) are present in relation or may if Either (a,b) or (b,a) is not present in relation. So in total, there are three possibilities.