# Finding the upper bound of states in Minimal Deterministic Finite Automata

I have a task to determine the upper bound of states in the Minimal Deterministic Finite Automata that recognizes the language: $$L(A_1) \backslash L(A_2)$$, where $$A_1$$ is a Deterministic Finite Automata(DFA) with $$n$$ states and $$A_2$$ is Non-deterministic Finite Automata(NFA) with $$m$$ states.

The way I am trying to solve the problem:

1. $$L(A_1) \backslash L(A_2) = L(A_1) \cap L(\Sigma^* \backslash L(A_2)$$, which is language, that is recognised by automata $$L’$$ with $$n*m$$ states
2. Determinization of $$L’$$ which has $$(n*m)^2$$ states and it is the upper bound of states.

Am I right?