T OR F

1.Let X and Y be infinite sets and suppose that there exists a function f from X to Y that is both one-to-one and onto.

Let g be any function from X to Y. Then g is one-to-one if and only if it is onto.

2.Let = {a, b} and consider the following functions from ^* to itself. If w = or w ends in a, let f(w) = wb. If w ends in b, let f(w) = wa. Let g() = and if w , let g(w) be the string obtained by deleting the last letter of w. Then f and g are inverses of one another.