1. Which of the following are equivalence relations? For those that are, describe the equivalence classes as best as you can. N a. On X = Zx yiff xy0 b. On X = Nay iff either (x > 100 and y> 100) or (<100 and y < 100) c. On X=Qxyiff x-yEN d. On X = Zx ~ yiff rye Z 2. For x, y ЄR, define x ~1 yiff x and y are both positive, both negative, or both 0. a. Show that b. Show that c. Show that is reflexive. is symmetric. is transitive. d. What is the equivalence class [1]? e. What is the equivalence class [-1]? f. What is the equivalence class 0? g. Show that every real number x is in exactly one of the classes [1], [-1] or [0].

1. Which of the following are equivalence relations? For those that are, describe the equivalence classes as best as you can. N a. On X = Zx yiff xy0 b. On X = Nay iff either (x > 100 and y> 100) or (<100 and y < 100) c. On X=Qxyiff x-yEN d. On X = Zx ~ yiff rye Z 2. For x, y ЄR, define x ~1 yiff x and y are both positive, both negative, or both 0. a. Show that b. Show that c. Show that is reflexive. is symmetric. is transitive. d. What is the equivalence class [1]? e. What is the equivalence class [-1]? f. What is the equivalence class 0? g. Show that every real number x is in exactly one of the classes [1], [-1] or [0].

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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