JEE Math Practice Question

Let $R$ be the set of real numbers. Statement I : $A=\{(x, y) \in R \times R: y-x$ is an integer $\}$ is an equivalence relation on $R$. Statement II : $ B=\{(x, y) \in R \times R: x=\alpha y$ for some rational number $\alpha\}$ is an equivalence relation on $R$.

1. A.Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
2. B.Statement I is true, Statement II is false.
3. C.Statement I is false, Statement II is true.
4. D.Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I.