Set A is the set of all books in the library of a college.R={x,y):x and y have the same number of pages }Now, R is reflexive since (x,x)∈R as x and x has the same number of pages.Let (x,y)∈R⇒x and y have the same number of pages.⇒y and x have the same number of pages.⇒(y,x)∈R∴R is symmetric.Now, let (x,y)∈R and (y,z)∈R⇒x and y and 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)∈R∴R is transitive.Hence, R is an equivalence relation.