By Kenneth A. Ross

Key profit: This ebook offers a legitimate mathematical remedy that raises easily in sophistication. Key themes: The e-book provides utility-grade discrete math instruments in order that any reader can comprehend them, use them, and circulation directly to extra complicated mathematical issues. marketplace: A convenient reference for laptop scientists.

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B) Find two other positive integers m and n such that +1 = 1 with I < s < lcm (m, n). @ ithe kne the0stuff;inQ~0Secio 0 12 % ma00Xthbose cause theousitef is;different Asyu can0 se b lipngtrog the book, te 's a lo ofSS? Wiea fyuwr rigt in: our cass. One of th skilsweca alwaysprati xli oaflo tdn mr is wrtin idascl y Sota' ht the book eas we t sas"xli. Shw" prbal cl for :ittlemor loial rumn. We w : mehd 0 fpofi$ etos23ad24 l + we'lcalwhtw'r enowrigo ivnte yotei 16 Chapter 1 i Sets, Sequences, and Functions the very simplest problems, you won't be able to look back through the section and find an example to imitate.

12. Consider the sets f0, 1), (0, 1) and [0,1]. True or False. (a) {O, 11 C (0, 1) (b) f0, 11 C [0,1] (d) (0,1} C Z (c) (0,1) C [0,1] (e) [0, 1] c Z (f) [0, 1] C Q (g) 1/2 and 7r/4 are in f0, 11 (h) 1/2 and 7r/4 are in (0, 1) (i) 1/2 and 7r/4 are in [0, 1] 13. Consider the following three alphabets: E1 = fa, b, c), = {a, (2 b, ca}, and E3 = {a, b, Ab}. Determine to which of Z*, V, and E* each word below belongs, and give its length as a member of each set to which it belongs. , leftmost] letter of w is deleted, is the resulting string in E*?

A) Calculate f(3), f(1/3), f(-1/3), and f(-3). (b) Sketch a graph of f. (c) Find Im(f). 8. Let S = {1, 2, 3, 4, 51 and consider the functions IS, g, and h from S into S defined by Is(n) = n, f(n) 6-n, g(n) = max{3, n}, and h(n) = max{l, n - 1}. , list the elements in their graphs. (b) Sketch a graph of each of these functions. 9. [(-1)n + 1]. The function f is the characteristic function for some subset of 2. Which subset? 10. Consider subsets A and B of a set S. (a) The function XA XB is the characteristic function of some subset of S.