I have observed the below statement in a report.
$ f(x,y) = \left\{ \begin{array}{lr} f<0 & : (x,y) \in A\\ f = 0 & : (x,y) \in B \\ f>0 & : (x,y) \in C \end{array} \right.$
I understand the meaning behind it, but is the notation correct? And in this case how do I write the statement then?