Let $A=$Set of all book in library in college. Given $R=$ {$(x,y):x$ and $y$ have same number of pages}:

If $x=y$, such that $(x,x) \in R$, then $x$ and $y$ have the same number of pages. Hence, $R$ is reflexive.

For $R$ to be symmetric, $(x,y) \in R \; \Rightarrow \; (y,x) \in R$

If $x$ has same number of pages as $y$ then $y$ also has same number pages as $x$. Therefore, $R$ is symmetric

For $R$ to be transitive, if $(x,y),(y,z) \in R \; \Rightarrow \; (x,z) \in R$

If x and y have same number of pages and y and z have same number of pages Then x and z also have same number of pages. Hence R is transitive

Hence R is an equivalance relation.