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

• A

  both $R_1$ and $R_2$ are transitive relations
• Correct answer
  B

  range of $R_2$ is $\left\{1,2,3,4\right\}$
• C

  range of $R_1$ is $\left\{2,4,8\right\}$
• D

  both $R_1$ and $R_2$ are symmetric relations

Hence, the correct answer is option: 'B'.