Sets, Relations and Function: Let N denote the set of all natural numbers. Define two binary… | JEE Main 2018

JEE Main 2018 (Online) 16th AprilQuestion 1

Let $N$ denote the set of all natural numbers. Define two binary relations on $N$ as $R_1=\{(x,y)\in N\times N: 2x+y=10\}$ and $R_2=\{(x,y)\in N\times N: x+2y=10\}$. Then

Sets, Relations and Function

both $R_1$ and $R_2$ are transitive relationsrange of $R_2$ is $\{1,2,3,4\}$✓ Correct answerrange of $R_1$ is $\{2,4,8\}$both $R_1$ and $R_2$ are symmetric relations

Solution

$R_1=\{(1,8),(2,6),(3,4),(4,2)\}$, range $\{2,4,6,8\}$; $R_2=\{(8,1),(6,2),(4,3),(2,4)\}$, range $\{1,2,3,4\}$. Neither is symmetric and $R_1$ is not transitive. Range of $R_2$ is $\{1,2,3,4\}$.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2018 (Online) 16th April)

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