Further, there are some elements like e and f in X2 which are not images of
any element of X1 under f1, while all elements of X3 are images of some elements of X1
under f3 The above observations lead to the following definitions:
Definition 5 A function f : X → Y is defined to be one-one (or injective), if the images
of distinct elements of X under f are distinct, i e , for every x1, x2 ∈ X, f(x1) = f(x2)
implies x1 = x2