Let $A = \{ 0,1,2,\ldots.9)$. Let R be a relation on A defined by $(x,y) \in R$ if and only if $|x -

Question

Let $A = \{ 0,1,2,\ldots.9)$. Let R be a relation on A defined by $(x,y) \in R$ if and only if $|x - y|$ is a multiple of 3.

Given below are two statements:

Statement I: $n(R) = 36$

Statement II: $R$ is an equivalence relation.

In the light of the above statements, choose the correct answer from the options given below

Accepted Answer

Number of form $3	ext{ }K = 4$Number of form $3	ext{ }K + 1 = 3$Number of form $3	ext{ }K + 2 = 4$$4 	imes 4 + 3 	imes 3 + 3 	imes 3 = 34$ relations$${\Rightarrow xRy \Rightarrow yRx }{\Rightarrow (x - y) = 3\lambda,(y - z) = 3\mu }{\Rightarrow (x - z) = 3(\lambda + \mu) }$$R is reflexive, symmetric and transitive $S_{2}$ is ture Ans. $S_{1}$ is false but $S_{2}$ is ture

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