3. (10 points) Consider the language L of odd length strings over the alphabet {a, b, c such that the middle symbol is b. For example, acbca, b, aabca are in L but bb, acb, a are not in L. Fill in the missing parts of the following proof to show that L is not regular Assume (towards a contradiction) that L is regular. Then the Pumping Lemma applies to L. Let p be the pumping length of L. Choose s to be the string Since this string is in L and has length greater than or equal to p, the Pumping Lemma guarantees s can be divided into parts szyz such that for any i 2 0, yz is in L, and that ly>0 and ay p. But if we let i = , we get a string ry'z that is not in L because This is a contradiction. Therefore the assumption is false, and L is not regular Created by Paint X