- #1

Jairo Rojas

- 17

- 0

## Homework Statement

. Let A be a set and {B1, B2, B3} a partition of A. Assume {C11, C12} is a partition of B1, {C21, C22} is a partition of B2 and {C31, C32} is a partition of B3. Prove that {C11, C12, C21, C22, C31, C32} is a partition of A.

## Homework Equations

## The Attempt at a Solution

I know this problem looks a little bit intuitive but I just want to make sure I make sense

proof

so {C11, C12, C21, C22, C31, C32} is a partition of A because A is divided into 3 disjoint subsets which make a partition of A, B1,B2,B3. And then each subset of these 3 disjoint subsets is further divided into two disjoint subsets which make a partition of the parent subset. So all elements in the parent subsets will make a partition of A because every element in each parent subset are disjoint among the elements of every other parent subset.