1. The problem statement, all variables and given/known data Hello, I need some help on the following. Im BRAND new to set theory and this was in my first HW assignment and Im not sure where to start. The question is as follows: Let A and B be parts of a set E Let [tex]P(E)\rightarrow P(A) X P(B)[/tex] be defined by [tex]f(X)=(A\cap X,B\cap X)[/tex] Show that f is injective if and only if [tex]A\cup B=E[/tex] Show that f is surjective if and only if [tex]A\cap B=\varnothing[/tex] notation: P(A) denotes the set of all parts of A 2. Relevant equations None 3. The attempt at a solution I do not have anything in my notes that remotely resembles this. Any pointers on how I should get started? Remember: Im new to set theory.