Relations And Its Types

Before knowing about Relations and its types, it is important to know about the function.

Relations and functions:

In our day to day life, there exists a relationship among various things. Like the rainfall how depends upon the evaporation, acceleration of a vehicle depends upon its velocity and there are so many examples. Similarly, relation in mathematics defines the relationship between two different sets of information.

Every day when you go for morning assembly in your school, you are supposed to stand in a queue in ascending order of the heights of all the students. This defines an ordered relation between the student and his height.

Therefore, we can say,

‘A set of ordered pairs is defined as a relation.’

Relations And Functions

This mapping depicts a relation from set A into set B. A relation from A to B is a subset of.The ordered pairs are (1,c),(2,n),(5,a),(7,n).For defining a relation, we use the notation where .

The set {1, 2, 5, 7} represents the domain.

The set {a, c, n} represents the range.

Relations and its types: (Reflexive Symmetric and Transitive Relation)

Reflexive Relation: is a relation in such that for every , then is a reflexive relation. In simpler terms, if every element maps to itself then it defines a reflexive relation.

Symmetric Relation: A relation R in set A is such that, R is said to be a symmetric relation. If a=b then for a symmetric relation b=a is also true.

Transitive Relation: A relation R in set A is said to be transitive when and implies that.

Equivalence Relation: If a relation is reflexive, symmetric and transitive at the same time it is known as an equivalence relation.
Let us go through an example to understand the concept of reflexive symmetric and transitive relations.

Example: Let A be the set of all the Honda city cars manufactured by Honda. A relation in set A is given by caris congruent to car Determine whether the defined relation is reflexive, symmetric and transitive.

Solution: Since all cars of the same design are same in shape and size, we can say that for every, .Therefore it represents a reflexive relation. Now for every, and b=a as the cars are exactly same. Hence, R is symmetric. Also some other car c of the same model will also be equal to car a and b. It implies that ⇒. It is also transitive.

Hence, R is an equivalence relation.

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Practise This Question

Let P = {(x,y) x2+y2=1,x,yR}. Then P is.