Answer:
We say that a function [tex]f:A\rightarrow B[/tex] is surjective or onto if and only if for every element [tex]b\in B[/tex] there exist an element [tex]a\in A[/tex], such that [tex]b=f(a)[/tex].
This definition says that a function is surjective if every element of [tex]B[/tex] has a pre-image, or that the image of [tex]A[/tex] by [tex]f[/tex] ‘‘fills’’ [tex]B[/tex] completely.
So, if the function [tex]f[/tex] is not surjective, there is, at least, one element of [tex]B[/tex] without pre-image. In other words, that we a have a proper inclusion [tex]f(A)\subset B[/tex], and [tex]f(A)\neq B[/tex] .
Step-by-step explanation:
