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Discrete Mathematics with Graph Theory (3rd Edition) 60

# Discrete Mathematics with Graph Theory (3rd Edition) 60 -...

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58 Solutions to Exercises (b) 0 = {x E R I f{x) = f{O) = O} = [0,1); 7/5 = [1,2) since L7/5J = 1; -3/4 = [-1,0) since L -3/4J = -1. (c) I = {I}; 2 = {2, 3, 6}; 4 = {4}; 5 = {5}. 28. (a) [BB] Here are the functions X -+ Y: ({a, 1), {b, In ({a, 1), {b, 2n ({a, 1), {b, 3n ({a, 2), {b, In ({a, 2), {b, 2n ({a, 2), {b, 3n ({a, 3), {b, In ({a, 3), {b, 2n ({a, 3), {b, 3n. Here are the functions Y -+ X: {{I,a),{2,a),{3,a)} {{I,a),{2,a),{3,b)} ({I, a), (2, b), {3, an ({I, a), (2, b), {3, bn ({I, b), (2, a), {3, an ({I, b), (2, a), {3, bn ({I, b), (2, b), {3, an ({I, b), (2, b), {3, bn. (b) [BB] There are no one-to-one functions Y -+ X. The one-to-one functions from X -+ Y are ({a, 1), {b, 2n ({a, 1), {b, 3n ({a, 2), {b, In ({a, 2), {b, 3n ({a, 3), {b, In ({a, 3), {b, 2n. (c) [BB] There are no onto functions X -+ Y. The onto functions Y -+ X are ({I, a), (2, a), {3, bn ({I, a), (2, b), {3, an ({I, a), (2, b), {3, bn ({I, b), (2, a), {3, an ({I, b), (2, a), {3, b)J ({I, b), (2, b), {3, an. 29. (a) There are no one-to-one functions Y -+ X. Here are the 24 one-to-one functions X -+ Y. ({a, 1), (b, 2), {c, 3n ({a, 1), (b, 2), {c, 4n ({a, 1), (b, 3), {c, 2n ({a, 1), (b, 3), {c, 4n ({a, 1), (b, 4), {c, 2n ({a, 1), (b, 4), {c, 3n ({a, 2), (b, 3), {c, In ({a, 2), (b, 3), {c, 4n ({a, 2), (b, 4), {c, In ({a, 2), (b, 4), {c, 3n ({a, 2), (b, 1), (c, 3n ({a, 2), (b, 1), {c, 4n ({a, 3), (b, 1), {c, 2n ({a, 3), (b, 1), {c, 4n ({a, 4), (b, 1), {c, 2n
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