Consider the following languages over the alphabet {a,b}. For each, give a proof for why they are not regular. (a) The set of words in which the number of a's is at least twice the number of bs. (b) {abm : n > m >0}. (c) The set of words that are palindromes (in other words, words w such that w = WR). (d) The set of words w that contain a string of at least consecutive as where n is the length of w