Question

The maximum number of identity relations = 1 .How ?Also describe about identity relations .

Answer 1

An identity relation on a set 'A' is the set of order pairs (a,a) where 'a' belongs to set 'A'.

For example: suppose A={1,2,3}, then the set of ordered pairs {(1,1), (2,2), (3,3)} is the identity relation on set 'A'.

Any relation 'R' on set 'A' is said to be reflexive if (a,a) belongs to R for every a belong to set 'A'.

For example: if A ={1,2,3}

Then a Relation R= {(1,1),(2,2),(3,3),(1,3),(3,2)} is a reflexive relation.

There can be many reflexive relation defined. But an identity relation on any set is unique.

$\Rightarrow$ In identity relation, every element is related to itself only. Then the relation R={(x,x): x \in A} on A is called the identity relation.

And Maximum number of identity relation is 1.