Let ∑ = {a, b}, and let L be the language over ∑: L ={ w € ∑+ |w is even, and w contains at least one a in the first half and exactly one b in the second half }
Give a context-free grammar (CFG) for L, and briefly explain how it works to correctly represent the language. There are no additional requirements for your solution other than what is stated here, except the usual guidance to make sure your answer is clear and understandable and avoids too much unnecessary complexity. In particular, there is no credit for the grammar being unambiguous (if possible.)