Solve this following

Question:

Let $\mathrm{R}$ be the set of real numbers.

Statement-1: $A=\{(x, y) \in R \quad R: y-x$ is an integer $\}$ is an equivalence relation on $R$.

Statement-2: $B=\{(x, y) \in R \quad R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $\mathrm{R}$.

 

  1. Statement- 1 is true, Statement- 2 is false.

  2. Statement- 1 is false, Statement- 2 is true

  3. Statement- 1 is true, Statement- 2 is true; Statement- 2 is a correct explanation for Statement- 1

  4. Statement- 1 is true, Statement- 2 is true; Statement- 2 is not a correct explanation for Statement- 1


Correct Option: 1

Solution:

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