5. (10 points) The Only Question that counts. For a word we {a,b}*, let counta(w) and count(w) denote the number of occurrences of a and b in w, respectively. (a) Show that the set X = {w {a,b}* : counta(w) = {w E {a,b}* : counta(w) = 2 county(w)} corresponds to the language of the grammar S aSaSbSlaSbSaS|6SaSaSje. (b) Does the grammar S +aSaSbaSbSa|6SaSaSe generate the same language as X? Prove or give a counterexample