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 Rationalised 2023-24
RELATIONS AND FUNCTIONS
15
Solution Clearly IN is onto