Question

What are the identity relation on $ setA = \left\{ {a,b,c} \right\} $ .

Answer 1

Hint: If every element on $ setA $ belongs to itself, then it is called the identity relation. For example, $ setB = \left\{ {1,2,3} \right\} $ , then the identity relation on $ setB $ is $ \left\{ {\left( {1,1} \right),\left( {2,2} \right),\left( {3,3} \right)} \right\} $ , here every element is related to itself. On any set, the identity relation is unique.

Complete step by step answer:
In this problem, we have to find the identity relation on $ setA = \left\{ {a,b,c} \right\} $ , as we know in identity relation every element of set is related to itself and makes it unique. So, the identity relation of the $ setA = \left\{ {a,b,c} \right\} $ is $ \left\{ {(a,a),(b,b),(c,c)} \right\} $ . We can also define identity relation as the set of ordered pairs.
Additional Information: There are many types of relations i.e. Empty relation, Universal relation, Identity relation, Inverse relation, reflexive relation, symmetric relation, transitive relation and equivalence relation and also there are many types of set i.e. Singleton set, empty set, proper set, power set, finite set, infinite set, universal set and equal set.

Note: A collection of well-defined objects is termed as a set. All elements of the set are listed inside the curly brackets and the set is represented by a capital letter. Every element of a set belongs to the defined set. As in $ setA = \left\{ {a,b,c} \right\} $ , a, b, c all belongs to $ setA $ . Here, all objects are grouped in a set. In $ setA $ , a is an element which should be denoted by ‘ $ a \in A $ ’, which means ‘a’ belongs to ‘A’. We can also denote other elements as ‘ $ b \in A $ ’,means ‘b’ belongs to ‘A’ and ‘ $ c \in A $ ’, means ‘c’ belongs to ‘A’. $ $