Is my mathematical formulation correct?

Question

I have an input graph as below.

I am trying to represent the above pictorial representation in mathematical terms.

The above pictorial representation can be viewed as a function from X to P (Y), where P (Y) represents the powerset of Y. P (Y) represents the set of all subsets of Y.

Is my above mathematical formulation correct for the given picture?

Answer 1

The above is correct.

Denote the function as $f$.

Then,for example: $$f(A_{1})=\{L_{1},L_{2}\} ,f(A_{5})=\emptyset$$