I've been stuck on this question for a while now and was hoping someone might be able to give me some help cause i don't really understand it.
Let B be a set. Define what it means to say that
B1,B2 give a partition of B, where B1 and B2 are subsets of B. Let
f : A −→ B be a function. Suppose that C is a subset of B. Write down
the definition of f−1(C). Suppose that B1,B2 is a partition of B. Prove,
using your definitions, that f−1(B1), f−1(B2) is a partition of A