Show that the following languages are not regular. You can use the pumping lemma game, or you can use closure properties (or both). (a) {w {a,b,c} | num(a,w) = num(b,w) + num(c,w)} In this problem num(a,w) means the number of a characters in the string w. (b) {aⁿ b^mc^k | n = m or m = k} (c) {w {a,b} | the length of w is a square number} This language contains all strings of length 1, 4, 9, 16, etc. Hint: after you pump, you'll want to show that the length of the resulting string is not a square. The best way to do this is to show that its length is strictly between consecutive squares n2 and (n + 1)2 for some appropriate n. (d) {w {a,b} | w , rev(w)}. In this problem rev(w) denotes the reverse of w (i.e., characters put in opposite order).