Partitions and definitions

Am i doing this right? And in the case of (c) how do you prove it?

Let B be a set.

a) Define what it means to say that give a partition of B, where are subsets of B.

b) Let f:A -> B be a function. Suppose that C is a subset of B. Write down the definition of .

c) Suppose that is a partition of B. Prove, using your definitions, that is a partition of A.

What i think the answers are...

a) i) are non-empty

ii) since 1 is not equal to 2,

iii) The U thing goes from i=1 to n but im not sure how to do that (does n=2?)

b)

c) ?

Am i right so far and if so how is c done?