3. [10 marks Eventually bounded. Let f NR20. We say that f is eventually bounded if and only if Note: We will not be marking translations into predicate logic for this question, but we still strongly recommend doing this as a first step for each proof/disproof. (a) Prove that the function f(n) i (b) Prove that every strictly decreasing function f : N R20 is eventually bounded. Note that we eventually bounded use the same definition of strictly decreasing as in Problem Set 1, except the function's domain and range are different here. (c) For any two functions f.g NR20, we define their product function to be the function fx g NR20 as follows: (f x g)(n)-f(n).g(n here n EN Prove that for every two eventually bounded functions fi, J2 :NR20 the function fi x f2 is also eventually bounded