Thus, the only
equivalence relation bigger than R1 is the universal relation This shows that the total
number of equivalence relations containing (1, 2) and (2, 1) is two Example 25 Consider the identity function IN : N → N defined as IN (x) = x ∀ x ∈ N Show that although IN is onto but IN + IN : N → N defined as
(IN + IN) (x) = IN (x) + IN (x) = x + x = 2x is not onto