Design a pda recognizing each of the following languages:
(1) {w | w = a nb n , n is odd}
(2) {w | w = w r and length of w is odd }
(3) {w | w = a nb 2n , n ≥ 1 }
(4) {w | w = a nb n+mc m, n ≥ 0, m ≥ 1 }
(5) {w | w = a 2nb 3n , n ≥ 0 }
(6) {w | w = a nb m, n ≥ 1, m ≥ 1 and n 6= m }