These are short answer questions concerning the pumping lemma for regular sets. assume that we are in the middle of a pumping lemma proof designed to show that a language is not regular, and that the value "n" and all other preliminaries have been determined. the questions below address specifically the "w" string, chosen in step 2 of the proof, and the "i" value, chosen in step 4 of the proof. let l = {0i1j0k | i, j,k > = 0 and i< =3k}(i) if w = 0n1n0n, what is the minimum "i" value that will work? give an argument to show that your "i" value is correct. will i=0 work? why or why not? (ii) if w = 0n1n02n, what is the minimum "i" value that will work? give an argument to show that your "i" value is correct. will i=0 work? why or why not? (iii) if w = 03n1n0n, what is the minimum "i" value that will work? give an argument to show that your "i" value is correct.(iv) if w = 02n1n03n, what is the minimum "i" value that will work, and why? (v) is w = 03n1n0n an acceptable "w" string? why or why not?