# Answer the questions in the space provided below. 1. The definition of a function f: X...

###### Question: Answer the questions in the space provided below. 1. The definition of a function f: X + Y is as a certain subset of the product X x Y. Let f: N + N be the function defined by the equation f(n) = n2. For each pair (x, y) listed below, determine whether or not (x,y) ef. a) (2,4) b) (5, 23) c) (1,1) d) (-3,9) 2. For each function defined below, state whether it is injective (one-to-one) and whether it is surjective (onto). You do not need to justify your answers. (a) g: Nx N + N defined by g(m, n) = 2m3". (b) f:NxN+Z+ defined by f(n,k) = nk. 3. Invent a function f satisfying the following properties. Be sure to state the domain and codomain of your function. the domain of f is an infinite set, f is surjective, • the codomain of f is an infinite set, • f is not injective.

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