I have encountered this problem in my studies and to be honest with you, I am just having some trouble grasping the notation. I have reread the section in my textbook and consulted a few of my peers, but I have yet to understand. I figured I would just give a shot to posting it here to see if I gain any insight. I apologize if this is not welcome, but I thought I would give it a try. Thank you much!
Consider the function $f \colon \mathbb Z\times \mathbb Z \to \mathscr P(\mathbb Z)$ defined by $f(a,b) = \{a,b\}$ As usual, $\mathscr P(\mathbb Z)$ denotes the power set of the integers $\mathbb Z$
a) Give a specific example to show $f$ is not one-to-one
b) Give a specific example to show $f$ is not onto