Please show work.

QUESTION 1 Given two languages L ={A, a, b} and M ={aa, A}, which of the following is the product of Land M? {aa aaa, baa, b) {aa, aaa, baa,b,a} {aa aaa, baa,} {aa aaa, baa, b.Aab} QUESTION 2 Use your wits to solve the following language equation for the unknown language L {A, a, ab} = {A, b, a, ab, aab, abb, abab} O AL= {Ab. ab) B.L = {b, ba} OC.L = {4, b. ba} OD.L = (b. ab) QUESTION 3 Find the number of strings over the alphabet {a, b, c, d} that satisfy the following condition Length 4, begins with a or c and ends with borc A. 4 x 4 x 4 x 4 = 256 B. 1 x 4 x 4 x 1 = 16 OC.1 x 4x4 x 2 = 32 OD.2 X 4 X 4 X 2 = 64