(a) Design a context-free grammar for the language L = { avc (ac) | i, j 0, v {a,b}*} over the alphabet = {a,b,c,}. Your grammar must have at most 3 variables and at most 7 rules. Clearly state the variables, the terminals, the rules, and the start variable for your grammar. You need not formally prove your grammar correct, but you should give a brief, coherent, convincing explanation of its correctness (in case of errors, such an explanation may also secure you partial credit). = (b) Consider the context-free grammar G {a, b, c} and R consists of the rules (V, E, R, S) where V S ASA | B A a b B BC | E Ca|b|c = {S, A, B, C'}, = Describe L(G). You need not formally prove your answer correct, but you should again give a brief, coherent, convincing explanation of how you obtained you answer (in case of errors, such an explanation may also secure you partial credit).