Let X a b c d let Y x y z and define f XSolutiona F is not

Let X = {a, b, c, d), let Y = {x, y, z}, and define f: X

Solution

a)

F is not one to one because
when x = a , y = z
and
when x = d , y = z

Since for different values of x, we have the same value of y, the function F defined by the arrow diagram is NOT one-to-one

b)

A function f from a set A to a set B is said to be onto(surjective) , if and only if for every element y of B , there is a corresponding element x in A

In the given arrow diagram, in the set, Y, the element \'x\' is not mapped onto anything from the domain, X.
Element y is mapped onto both b and c
Element z is mapped onto both a and d
But element x is not mapped onto anything

So, function F is NOT ONTO