Let X = R – (0,0) and - be defined over X by setting x-y - y = tx for some non-zero ! E R. (a) classes of X induced by -. Prove that - is an equivalence relation on X and describe the set X/ ~ of equivalence (b) relation - as above. Describe the set S'/~ of equivalence classes of S' induced by ~. (c) element of the equivalence class with respect to the dictionary order. Sketch a graph of all the representative points of all equivalence classes of S'/~. Given a equivalence class [r] € S'/ ~, choose its representative r to be the largest
Let X = R – (0,0) and - be defined over X by setting x-y - y = tx for some non-zero ! E R. (a) classes of X induced by -. Prove that - is an equivalence relation on X and describe the set X/ ~ of equivalence (b) relation - as above. Describe the set S'/~ of equivalence classes of S' induced by ~. (c) element of the equivalence class with respect to the dictionary order. Sketch a graph of all the representative points of all equivalence classes of S'/~. Given a equivalence class [r] € S'/ ~, choose its representative r to be the largest
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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answer a only
![2. Let X = R? - (0.0) and - be defined over X by setting
x -y = y = tx
for some non-zerol E R.
(a)
classes of X induced by -.
Prove that - is an equivalence relation on X and describe the set X/ ~ of equivalence
Let S' = {x € R? : ||x|| = 1} C X, and endow S' with the same equivalence
(ь)
relation - as above. Describe the set S'/~ of equivalence classes of S' induced by v.
(c)
element of the equivalence class with respect to the dictionary order. Sketch a graph of all the
representative points of all equivalence classes of S'/~.
Given a equivalence class [r] € S'/ ~, choose its representative r to be the largest](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F47d4f3e4-a83c-4f8d-b768-34b8f144d14c%2Fe27b0aee-f9c9-42f5-b023-008549c6b2a2%2F5jxjlmj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Let X = R? - (0.0) and - be defined over X by setting
x -y = y = tx
for some non-zerol E R.
(a)
classes of X induced by -.
Prove that - is an equivalence relation on X and describe the set X/ ~ of equivalence
Let S' = {x € R? : ||x|| = 1} C X, and endow S' with the same equivalence
(ь)
relation - as above. Describe the set S'/~ of equivalence classes of S' induced by v.
(c)
element of the equivalence class with respect to the dictionary order. Sketch a graph of all the
representative points of all equivalence classes of S'/~.
Given a equivalence class [r] € S'/ ~, choose its representative r to be the largest
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