Problem 1 [3 points] Let A, B be regular languages over alphabet . Is the following language regular? Prove your answer. A = {z|z & A,z 4 B} Problem 2 (3 points) Let C be a language defined over alphabet {0,1} as follows. Is C regular? Prove your answer. C = The set of strings with equal number of 010's and 101's Problem 3 (5 points) Construct a NFA for the following language defined over = {0,1}. D= {010M 109|n, n, q N, q = nm (mod 5)} Problem 4 [5 points) Prove that the following language defined over = {0,1} is not regular. E = {x|x = 079, where p, q are prime numbers}