question_answer 7)

Show that the relation R in the set A of all the book in a library of a college given by R = {(x, y) : x and y have same number of pages} is an equivalence relation. 

Answer:

R = {(x, y) : x and y have same number of pages} Reflexive : As a and a have the same number of pages             is reflexive. Symmetric : (a, b)  and b have the same number of pages        b and a have also the same number of pages        (a, b)  R and (b, a)        R is symmetric. Transitive : (a, b)  and b have the same number of pages.       (b, c)  and c have the same number of pages        have the same number of pages              is transitive.       Hence R is an equivalence relation.