You are correct in parts a & b.
However, part c is not necessarily true.
If the function is surjective (onto), then it is true.
If is not surjective define . That is a partition of .
It is counter-example to part c.
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?