Let A = {1, 2, 3, 4}. Examine which of the following relations is a function from A to A ?
(i) f = {(1, 1), (2, 3), (3, 4), (4, 4)}
(ii) g = {1, 4), (2, 3), (3, 4)}

Explanation

Given A = {1, 2, 3, 4}
(i) f = {(1, 1), (2, 3), (3, 4), (4, 4)}
Since no two first elements of ordered pairs are same, and all the elements of A have unique image, therefore f is a function.
(ii) g = {(1, 4), (2, 3), (3, 4)}
Since there is no mage in g corresponding to 4 of A
`:.` g is not a function.