Answer :

It is given that the set A of all the books in a library of a college. Then,

R = {(x, y): x and y have same number of pages}


Now, R is reflexive


Since, (x,x) ϵ R as x and x have same number of pages.


Let (x,x) ϵ R


x and y have the same number of pages


y and x have the same number of pages.


(y,x) ϵ R


Therefore, R is symmetric.


Now, let (x,y) ϵ R and (y,z) ϵ R


x and y have the same number of pages and y and z have the same number of pages.


x and z have the same number of pages.


(x,z) ϵ R


Therefore, R is transitive.


Therefore, R is an equivalence relation.


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