Let A = {w|w begins with a 1 and ends with a 0} and B = {w|w contains at least three 1s}.

(a) First, give two DFAs MA and MB that recognize A and B.

(b) Then use the union construction explained in Theorem 1.25 in our textbook to combine MA and MB into a single DFA called MC that recognizes the language C = {w|w begins with a 1 and ends with a 0, or contains at least three 1s}. Show both the formal definition and the state diagram of your machine