This question further tests your understanding of the subtleties of the Pumping Lemma: (a) [5 marks] Let B-of1rOk l k > 1 and r E *). Give a formal proof that Bi is not a regular language. (b) [5 marks] Let B oo k 1 and .Show that B2 is a regular language (c) We just proved in part (b) above that B2 is regular. Consider now the following argument, which claims to prove that B2 is, in fact, not regular Assume B2 is regular, and let p be the pumping length. Consider string s010 E B2, and decompose it as 8 =y: with r = , y = 0". z = 10. Then, pumping s down by setting i = 0 yields string syg B2. Hence, by the Pumping Lemma, we have a contradiction. We conclude that B2 is not regular. i. [3 marks] What is wrong with this proof