Exercise 4 (Ex. 10, Chapter 2 of [Martin; 2011]). Let M1 and M2 be the finite automata pictured below with their accepting languages L1 and L2. Draw the finite automata for L1L2,L1L2, and L1L2. (a) (b) Exercise 5 (Ex. 12, Chapter 2 of [Martin; 2011]). For each of the following languages, draw an FA accepting it. a. {a,b}{a} b. {bb,ba} c. {a,b}{b,aa}{a,b} d. {bbb,baa}{a} e. {a}{b}{a}{a}{b}{a} f. {a,b}{ab,bba} g. {b,bba}{a} h. {aba,aa}{ba} Exercise 6 (Ex. 17, Chapter 2 of [Martin; 2011]). Let L be the language AnBn={anbnn0}. a. Find two distinct strings x and y in {a,b} that are not L-distinguishable. b. Find an infinite set of pairwise L-distinguishable strings. Exercise 7 (Ex. 22, Chapter 1 of [Martin; 2011]). Using the pumping lemma, show that the below languages are not regular: L={anba2nn0}L={aibjj=iorj=2i} Exercise 8 (Ex. 38, Chapter 1 of [Martin; 2011]). In each part, find every possible language L{a,b} for which the equivalence classes of IL are the three given sets. {a,b}{b},{a,b}{ba},{,a}{a,b}{aa} {},{a}({b}{a}{a}{b}),{b}({a}{b}{b}{a})