6. (8 marks) For any positive integer n, let Sn denote the set of nonempty subsets of {1,2,... , n) For example, S3 - 113,{2), 13], 11,2), {1,3], (2, 3), {1,2,3]). For any nonempty set of positive integers X, let (X) denote the product of the elements of X. For example, if X {1, 2, 4,5) then (X)-40. Now, for any positive integer n, we define T(X) XESn For example o(3) 1 231.21-32.31.2-3 1 '232 36 6 Find a simplified expression for (n) for all positive integers n and prove your result using mathematical induction. 7, (6 marks) Define function H : R R > R R as follows: H(z, y) = (x+ 1, 2-y) for all (z,y) R R (a) Is H one-to-one? Prove or give a counterexample (b) Is H onto? Prove or give a counterexample