3. Designing context-free grammars and languages (a) Design a context-free grammar for the language 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 grainmar G = (V,L,R, S) where V- (S,A, B,C), = {a, b, c} and R consists of the rules 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)