Given the alphabet sigma = {a, b, c}, design a deterministic finite automaton (DFA) accepting the strings that contain either even numbers of a's, b's, and c's; or odd numbers of a's, b's, and c's. Minimize the number of states of the DFA obtained at Step 1 using both methods presented during the lectures. (Your DFA from Step 1 may already have a minimum number of states; if this is the case, you still have to justify it.)