Consider the set N²= NX N, the set of all ordered pairs (a, b) where a and b are natural numbers. Consider a function f: N² → N given by f((a, b)) = a + b. a. Let A = {(a, b) E N²: a, b ≤ 10}. Find f(A). b. Find f-1 (3) and f-¹({0,1,2,3}). c. Give geometric descriptions of f-1(n) and f-¹({0,1,..., n}) for any n ≥ 1. d. Find f¹(8) and If-¹({0,1,...,8})|.

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