Exercise 3. For each of the following languages, draw (if it exists) the state diagram of an automaton recognizing it. Test each automaton on two strings in the language, and two strings not in the language, plus the empty string. 1. w E 10,1 2. w E a, b 3. w E a, b contains an even number of zeroes) w has exactly three b's w has at least three a's and at least two b's) 4. w E 0, 1)* w contains 110 as a substring) 6. w E 0,1) is even ) 7. {w E [0,1 contains an equal number of 1' and '0