Which of the functions in exercise 1 of Section 51 are oneto

Which of the functions in exercise 1 of Section 5.1 are one-to-one? Which are onto?

Exercises
1. (a) Let A = {1, 2, 3}, B = {4}, and f = {(1, 4), (2, 4), (3, 4)}. Is f a
function from A to B?

Solution

Given a relation from A to B it is a function if and only if no element in A is mapped to two elements in B

We see that in f, all elements are mapped to 4 but no element gets mapped to two elements in B. So , if f is a function.

Since all three elements in A are mapped to 4 in B so f is not one-to-one

It is onto because B contains only one element ie 4 which is in image of f.