![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 π(X) denote the product of the elements of X. For example, if X {1, 2, 4,5) then π(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 σ(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.](https://d2vlcm61l7u1fs.cloudfront.net/media%2F7f8%2F7f87cf23-85b2-4d10-9d9a-f0df929feea0%2FphpADAVwS.png)
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(Solved) : 6 8 Marks Positive Integer N Let Sn Denote Set Nonempty Subsets 1 2 N Example S3 113 2 13 Q27589837 . . . .
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