Lét Y C R² be the set {(x, y)|0 < x < 1,0 < y <1 and y E Q if x # 0} endowed with the dictionary order. (a) Does Y have a smallest element? (b) Does Y have a largest element? (c) Sketch inside [0, 1] × [0, 1] the subset W = {(x, y) E Y| 1/2 < x < 3/4}.
Lét Y C R² be the set {(x, y)|0 < x < 1,0 < y <1 and y E Q if x # 0} endowed with the dictionary order. (a) Does Y have a smallest element? (b) Does Y have a largest element? (c) Sketch inside [0, 1] × [0, 1] the subset W = {(x, y) E Y| 1/2 < x < 3/4}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
PB 3
![Let Y C R² be the set
{(x, y)|0 < x < 1,0 < y <1 and y E Q if x + 0}
endowed with the dictionary order.
(a) Does Y have a smallest element?
(b) Does Y have a largest element?
(c) Sketch inside [0, 1] × [0, 1] the subset W = {(x, y) E Y| 1/2 < x < 3/4}.
(d) For (x, y), (w, z) E Y, declare (x, y)
equivalence relation on Y? If so, describe the set Z of equivalence classes of Y induced by ~,
and define a bijection from [0, 1] to Z.
(w, z) if and only if y
= z. Does ~ define an](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb6dd0c6-5527-4513-9258-707eb85d4bd1%2F0dde38a4-269e-43a9-b969-0cbc17264374%2Fheoineb_processed.png&w=3840&q=75)
Transcribed Image Text:Let Y C R² be the set
{(x, y)|0 < x < 1,0 < y <1 and y E Q if x + 0}
endowed with the dictionary order.
(a) Does Y have a smallest element?
(b) Does Y have a largest element?
(c) Sketch inside [0, 1] × [0, 1] the subset W = {(x, y) E Y| 1/2 < x < 3/4}.
(d) For (x, y), (w, z) E Y, declare (x, y)
equivalence relation on Y? If so, describe the set Z of equivalence classes of Y induced by ~,
and define a bijection from [0, 1] to Z.
(w, z) if and only if y
= z. Does ~ define an
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