(a) Prove that the language L = {12/3221} is not regular by using the Pumping Lemma. Use the string 1"2"32" and i = 3 at appropriate points in the proof. (b) Write out the proof of the same result which uses the string 132 and i=0 instead. Which steps are different? Which steps remain the same? (e) There are some errors in the proof below that the language L = {1'2' #32 @2'1'} is not context-free. Find and correct all such errors. The best way to do this is to write out the correct proof, highlighting the differences between the correct proof and the one below. Claim: The language L = {12 #32 @21'} is not context-free. Proof: Assume L2 is regular. Then the Pumping Lemma applics and so for some n1 such that for some w L such that wn, w = xyzuv where lyzu n y and u ry' zu've L for all i > 0 w= Choose w 12" 32" @2"1" and so we L and wn. So by the Pumping Lemma w = xyzuv = 12 #32@2"1" and lyzul