Answer to Question #179902 in Discrete Mathematics for Johnson

Question

 Let R be a relation over set A, then: Prove that IA∘R=R=R∘IA. 

Answer 1

As R is a relation on set A.

It implies that The elemnts of A must belong to the R in cartesian product form.

Taking LHS

$IA*R=A*R=R$

Since The product of the set on which relation is defined is equal to that relation.

Now taking LHS-

$R*IA=R*A=R$

This implies that-

$IA*R=R=R*IA$ , Hence proved.