# Power set of a set of sets

1. Sep 13, 2014

### cilla

How are you supposed to go about putting together the power set of a set of sets such as
X = {{1},{1,2}}

What is the power set of X then? And what's the rule for calculating cardinality for the power set of a set that consists of elements which are sets such as the above? Because the set X to my understanding has 2 elements, both of which are sets... so the power set of X doesn't consist of only 4 elements, does it?

There are:
{}, {1}, {1,2}, {{1},{1,2}}

Or is that really all?

2. Sep 13, 2014

### da_nang

Yep, that's about it. You only care about finding the subsets of $X$ so the element $a_i \in X$ can be whatever.

3. Sep 13, 2014

### gopher_p

Actually, the singletons of X here are {{1}} and {{1,2}}. It's a subtle but important distinction.

4. Sep 13, 2014

### cilla

Oh yes, thank you gopher_p (and da_nang). I'm just glad it's not some crazy mix of inner and outer elements.

5. Sep 14, 2014

### caveman1917

If the iterated set notation confuses you, just do something like $a = \{1\}, b = \{1, 2\}, X = \{a,b\}$ and then at the end substitute back.