Let R be the relation on R defined by xRy if there exists some n∈Zsuch that y=x⋅cny=x⋅cn. Let c = 6 and d be = 9 Let R be the relation on IR defined by x Ryif there exists some n e Z such that y = x · c".1. Show that R is an equivalence relation on R.2. What is [d]? Write your answer in the form [d] = {..., *, *, d, *, *,...}with at least 5 elements listed. You don't have3. Is there a singleton equivalence class? If yes, what is it? If no, explain why.4. Find at least one a e R such that [a] contains a rational number and an irrational number.explain your answer.

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Let R be the relation on R defined by xRy if there exists some n∈Zsuch that y=x⋅cny=x⋅cn. Let c = 6 and d be = 9

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

Let R be the relation on R defined by xRy if there exists some n∈Zsuch that y=x⋅cny=x⋅cn. Let c = 6 and d be = 9

Let R be the relation on IR defined by x Ryif there exists some n e Z such that y = x · c".
1. Show that R is an equivalence relation on R.
2. What is [d]? Write your answer in the form [d] = {..., *, *, d, *, *,...}with at least 5 elements listed. You don't have
3. Is there a singleton equivalence class? If yes, what is it? If no, explain why.
4. Find at least one a e R such that [a] contains a rational number and an irrational number.
explain your answer.

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