Please answer all questions!

This question develops your ability to design CFGs. For each of the following languages, give a CFG. Assume the alphabet is Sigma = {0, 1}. For string x = x_1x_2 ellipsis x_n, we define x^R:= x_n ellipsis X_2x_1, i.e. this operation reverses the order of the symbols in x. Justify your answers briefly. {x | x starts and ends with the same symbol}. {x |the length of x is odd}. {x| x = xR, that is, x is a palindrome}. Phi For this part, set E = {a, b, $}. The language is then {x_1Sx_2$ ellipsis $_x_k | k greaterthanorequalto 1, each x_I belong {a, b}^*, and for some I and j, x_i = x^R_j}