Consider the set $ K = \{ 2^n : n \in \mathbb{Z} \} $. The relation $ R $ on the set $ \mathbb{Q}^+ $ (the set of positive rational numbers) defined by $ x \, R \, y $ if and only if $ \frac{x}{y} \in K $, for $ x, y \in \mathbb{Q}^+ $, is an equivalence relation.

K=2n:n∈ℤ A relation R is said to be an equivalence relation if it is reflexive, symmetric and…

Answered: Consider the set K rational numbers)…

Consider the set K rational numbers) defined by x Ry if and only if E K, for x, y E Q+, is an equivalence relation. {2" : n E Z}. The relation R on the set Q+ (the set of positive

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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Consider the set $ K = \{ 2^n : n \in \mathbb{Z} \} $. The relation $ R $ on the set $ \mathbb{Q}^+ $ (the set of positive rational numbers) defined by $ x \, R \, y $ if and only if $ \frac{x}{y} \in K $, for $ x, y \in \mathbb{Q}^+ $, is an equivalence relation.

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#1. Let R be the relation defined on the set of all integers Z as follows: for all integers m and n, m R n e= m - n is divisible by 5. Prove that R is Equivalence Relation.
3. Let R be a relation defined on the set A = N × N where (a, b) R (c, d) if að = cd. Show R is an equivalence relation. Then, list the elements of the equivalence class [(9, 2)].
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Can you please help me with this question?