Sets, Relations and Function: Let R_1=\(a,b)inmathbfNtimesmathbfN:|a-b|le13\ and… | JEE Main 2022

JEE Main 2022 (Online) 28th June Evening ShiftQuestion 1

Let $R_1=\{(a,b)\in\mathbf{N}\times\mathbf{N}:|a-b|\le13\}$ and $R_2=\{(a,b)\in\mathbf{N}\times\mathbf{N}:|a-b|\neq13\}$. Then on $\mathbf{N}$ :

Sets, Relations and Function

Both $R_1$ and $R_2$ are equivalence relationsNeither $R_1$ nor $R_2$ is an equivalence relation✓ Correct answer$R_1$ is an equivalence relation but $R_2$ is not$R_2$ is an equivalence relation but $R_1$ is not

Solution

Both are reflexive and symmetric. $R_1$ not transitive: $(1,14),(14,27)\in R_1$ but $|1-27|=26>13$. $R_2$ not transitive: $(1,2),(2,14)\in R_2$ but $|1-14|=13$. Neither is an equivalence relation: option B.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2022 (Online) 28th June Evening Shift)

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