Thread: set partitions

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

is a partition of when:

1.
2.
3.

Denote as the disjunct union of .

If is a function and . You can write . Then .
Then we've shown that form a partition of .

The same way is shown that .

You simply need to show that satisfy conditions 1,2,3

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.

If you have a collection of nonempty subsets of B which are pairwise disjoint (any two distinct ones are disjoint), and the union of all these subsets is the set itself, then you know those subsets are partition of that set.

If and are (1) nonempty, (2) non-overlapping subsets and (3) , you know they are partitions of of the set . These 3 conditions are what partition means; for example gender partitions humanity.