Finding the subsets of an array in PHP

I have a Relational Schema with attributes (A B C D). I have a set of Functional Dependencies with me too.

Now I need to determine the closure for all the possible subsets of R's attributes. That's where I am stuck. I need to learn how to find subsets (non-repeating) in PHP.

My Array is stored like this.

$ATTRIBUTES = ('A', 'B', 'C', 'D').

so my subsets should be

$SUBSET = ('A', 'B', 'C', 'D', 'AB', 'AC', AD', 'BC', 'BD', 'CD', 'ABC', 'ABD', 'BCD', 'ABCD')

The code shouldn't be something big but for some reason I can't get my head around it.