(i) Each of the following apparently defines a function. However, each has one or more problems. Explain carefully what is wrong with each. (a) c : {cat, dog, rabbit, goat} → {black, brown, white, red} c(cat) = white, c(dog) = brown, c(rabbit) = brown, c(goat) = grey, c(cat) = black. (b) m : P({1,2, 3, ..., 100}) → {1,2, 3, . . , 100}, m(A) = the smallest element of A (ii) Let f and g be functions defined by f : R → R, g : N → N, g(x) = 5x – 4. f (x) = 5x – 4 (a) Prove carefully that f is bijective. (b) Prove carefully that a is not bijective.

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