GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 38

Answer 1

Detailed Video Solution: Video Solution with Complete Analysis

A binary relation $\mathrm{R}$ over a set $\mathrm{A}$ is called a Euclidean relation if for all $\mathrm{x}$, $y, z \in A$, if $x R y$ and $x R z$, then $y R z$. For example, the $\equiv k$ relation is Euclidean over $\mathbb{Z}$, but the $\leq$ relation over $\mathbb{N}$ is not.

Let $\mathrm{R}$ be an arbitrary binary relation over some set $\mathrm{A}$.

We can easily prove that $R$ is an equivalence relation if and only if it is reflexive and Euclidean.

Video Solution with Complete Analysis: https://www.youtube.com/watch?v=DEGoAIItx70

Comments

@Deepak Poonia sir here c always correct how option A and D r correct?

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if reflexive , then why not symmetric and transitive when elements are  within same set ??

no doubt the answer is  Option A,B,D .

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@Priyotosh2001, Reflexive relation does not imply Symmetric, Transitive.

Also, Reflexive & GO relation do imply Symmetric, Transitive. We have proven it in this Video Solution. 

@JayRathi, See this Detailed Video Solution.