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

solution:

Books x and x have same number of pages. (x, x) ∈ R. R is reflexive.

In the event that (x, y) ∈ R and (y, x) ∈ R, so R is symmetric.

Since, Books x and y have same number of pages and Books y and x have same number of pages.

Once more, (x, y) ∈ R and (y, z) ∈ R and (x, z) ∈ R. R is transitive. In this way, R is a comparability connection.