Suppose we are given DFAs MA, MB, and MC that accept languages A, B, and C, respectively. Explain how to use the automata constructions weve studied to obtain DFAs that accept each of the following languages.

(a) (A B) C

(b) (A B)

(c) (A B) C

(d) ((A B) ^c ) C

Let nA, nB, and nC be the number of states in MA, MB, and MC, respectively. In terms of nA, nB, and nC, how many states will each DFA have?

For simplicity, assume that the automaton resulting from each construction is taken without modification. In particular, inaccessible states are not removed. For example: if the subset construction is applied to a 5-state NFA, the resulting DFA has 32 states. While some of these states may be inaccessible and could be removed, assume that all 32 states are used in any subsequent construction involving the DFA