Understanding Relations of X, Y, C and P(x) in Sets

[ptex]

This is the example I am going by;
X={a,b,c,d} Y={c,d} C={b,c}
P(x)={{a,b,c},{a,b,d},{a,c,d}{b,c,d}
{a,b},{a,c},{a,d},{b,c},{b,d},{c,d},
{a},{b},{c},{d},{a,b,c,d},{}}
This next part I do not understand? AUY=BUY

A[sub]1[/sub]={a,c,d},{a,c},{a,d},{a}
A[sub]2[/sub]={a,b,c},{a,b,d},{a,d},{a,b,c,d}
A[sub]3[/sub]={b,c,d},{b,c},{b,d},{b} (=elements of C)
Y={c,d},{c},{d}

What I would like to understand is how she came up with A[sub]1[/sub], A[sub]2[/sub], A[sub]3[/sub], and Y? 
I know they are subsets but how?
I have been tring to figure this out for 3days and I just want to get it.

 

[mathman]

There is something missing in your problem statement. What are A and B?

 

[ptex]

It says A & B = anyone of the 16 subsets.

 

[ptex]

Is that any help?

 

[mathman]

If A and B are each anyone of subsets, then AUY=BUY would not be true in many cases. For example A={a} and B={b}. The part called code, A₁ etc., seems unrelated to the question before.