# Let N denote the set of all natural numbers. Define two binary relations on N as R1 = {(x, y) Î N × N : 2x + y = 10} and R2 = {(x, y) Î N × N : x + 2y = 10}. Then

Question:

Let $\mathrm{N}$ denote the set of all natural numbers. Define two binary relations on $N$ as $R_{1}=\{(x, y) \in N \times N: 2 x+y=10\}$ and $R_{2}=\{(x, y) \in N \times N: x+2 y=10\}$. Then

1. Both $R_{1}$ and $R_{2}$ are transitive relations

2. Both $R_{1}$ and $R_{2}$ are symmetric relations

3. Range of $R_{2}$ is $\{1,2,3,4\}$

4. Range of $R_{1}$ is $\{2,4,8\}$

Correct Option: 3

JEE Main Previous Year 1 Question of JEE Main from Mathematics Sets, Relations and Functions chapter.
JEE Main Previous Year Online April 16, 2018

Solution:

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