Construct a NFA whose language is the set of strings over {a, b, c, d} which do not contain all four symbols. Of course, by keeping track of which symbols we have seen so far, we can construct a DFA for this language using 24 = 16 states. Your solution should have at most 8 states, which will force you to exploit nondeterminism.

Argue your solution is correct. (Show that any string which does not contain all four symbols is accepted by your automaton, and also show that any string accepted by the automaton does not contain all four symbols.)