Question

Fill in the blank: A relation R in a set A is called ______ relation, if each element of A is related to every element of A, i.e., R = A × A.

Answer 1

Answer:

A relation R in a set A is called universal relation, if each element of A is related to every element of A, i.e., R = A × A.

Answer 2

Relation is commonly known as reflexive relation

Given

• relation R in a set A
• each element of A is related to every element

To find

• The common name of such relation.

Solution

we are provided with a relation in which each elements of the set are related to itself and we are asked to find out the common name that such a relation would have.

we know that such a relation is commonly known as reflexive relation

• it is a type of a relation where each element in set would be related to itself.

• That is, if a belongs to setA then, (a,a) should also belong to set A.

• It is important that a relation should be reflexi for it to be a equivalence class

It should be noted that for a relation to be equivalence class, the relation should be reflexive, symmetric as well as transistive.