Draw state-transition diagrams for each of the following finite state machines based on the attached Cayley table. de + i a b (a) The finite state machine whose associated monoid matches the table. [Hint: use multiplication on the left by a, b, or c as your input set] (b) The finite state machine whose states are the elements in the Cayley table to the right, but use conjugation by a, b, or c as the input set. For example, applying conjugation by a to e gives Cale) = a hea. ) [Hint: determine the inverses first] i a b c i a b de a d C f e i b g d a f b e dg f d e f g i a i gb a d f C i e b 8 f a i f g fg gb i e a i b f d a e d d e e 1 C f = g 09 60 cb Draw state-transition diagrams for each of the following finite state machines based on the attached Cayley table. de + i a b (a) The finite state machine whose associated monoid matches the table. [Hint: use multiplication on the left by a, b, or c as your input set] (b) The finite state machine whose states are the elements in the Cayley table to the right, but use conjugation by a, b, or c as the input set. For example, applying conjugation by a to e gives Cale) = a hea. ) [Hint: determine the inverses first] i a b c i a b de a d C f e i b g d a f b e dg f d e f g i a i gb a d f C i e b 8 f a i f g fg gb i e a i b f d a e d d e e 1 C f = g 09 60 cb