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R X R be ur ictionary rder relation, and consider its subset S onsisting oOf all the points on the unit circle centered at the origin. a. Let (a, b) E S. Describe the points (c, d) E S such that (a, b) < (c, d) and the points (e, f) E S such that (e, f) < (a, b). b. Does S have a smallest element? If yes, identify. If no, explain. c. Does S have a largest element? If yes, identify. If no, explain.

R X R be ur ictionary rder relation, and consider its subset S onsisting oOf all the points on the unit circle centered at the origin. a. Let (a, b) E S. Describe the points (c, d) E S such that (a, b) < (c, d) and the points (e, f) E S such that (e, f) < (a, b). b. Does S have a smallest element? If yes, identify. If no, explain. c. Does S have a largest element? If yes, identify. If no, explain.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.CT: Test
Problem 5CT: Let all of the lines named be coplanar. Make a drawing to reach a conclusion. a If rs and st, then...
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2. Let R x R be under the dictionary order relation, and consider its subset S consisting of all the points on the unit circle centered at the origin. a. Let (a, b) E S. Describe the points (c, d) E S such that (a, b) < (c, d) and the points (e, f) E S such that (e, f) < (a, b). b. Does S have a smallest element? If yes, identify. If no, explain. c. Does S have a largest element? If yes, identify. If no, explain. d. Let x = (, ) and y = (, 3). Describe the open interval (x, y). e. Does the open interval (x, y) in (d) above have a greatest lower bound? If yes, identify. If no, explain. f. Does the set S have the least upper bound property? Why or why not? g. Is the set S well-ordered? Why or why not?
Transcribed Image Text:2. Let R x R be under the dictionary order relation, and consider its subset S consisting of all the points on the unit circle centered at the origin. a. Let (a, b) E S. Describe the points (c, d) E S such that (a, b) < (c, d) and the points (e, f) E S such that (e, f) < (a, b). b. Does S have a smallest element? If yes, identify. If no, explain. c. Does S have a largest element? If yes, identify. If no, explain. d. Let x = (, ) and y = (, 3). Describe the open interval (x, y). e. Does the open interval (x, y) in (d) above have a greatest lower bound? If yes, identify. If no, explain. f. Does the set S have the least upper bound property? Why or why not? g. Is the set S well-ordered? Why or why not?
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