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4. Define a relation R on the x-y plane as follows: Given two points (X₁,Y₁) and (x2,Y2) in the x-y plane, (X1,Y1) R (X2 ,Y2) if and only if the distance between them is a whole number. Is R an equivalence relation? Prove or disprove.

4. Define a relation R on the x-y plane as follows: Given two points (X₁,Y₁) and (x2,Y2) in the x-y plane, (X1,Y1) R (X2 ,Y2) if and only if the distance between them is a whole number. Is R an equivalence relation? Prove or disprove.

Advanced Engineering Mathematics
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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**Problem Statement:** Define a relation \( R \) on the \( x\text{-}y \) plane as follows: Given two points \((x_1, y_1)\) and \((x_2, y_2)\) in the \( x\text{-}y \) plane, \((x_1, y_1) \, R \, (x_2, y_2)\) if and only if the distance between them is a whole number. **Question:** Is \( R \) an equivalence relation? Prove or disprove.
Transcribed Image Text:**Problem Statement:** Define a relation \( R \) on the \( x\text{-}y \) plane as follows: Given two points \((x_1, y_1)\) and \((x_2, y_2)\) in the \( x\text{-}y \) plane, \((x_1, y_1) \, R \, (x_2, y_2)\) if and only if the distance between them is a whole number. **Question:** Is \( R \) an equivalence relation? Prove or disprove.
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