1a) Let X be a set of numbers. Let Bin(X) denote the binary numbers corresponding to X, and let Unary(X) denote the numbers in X in unary. Fix X = {1, 2, 4, 8, 16, ..}. Is Bin(X) regular? Is Unary(X) regular? (If regular, give an NFA. If not regular, give a proof using pumping lemma)

1b)Sq(L) = {ww | w in L}. Sqrt(L) = {w | ww in L}. If L is regular is Sq(L) regular? If L is regular is Sqrt(L) regular? (If regular, describe how to construct an NFA. If not regular, give a proof of non-regularity)