Sets, Relations and Functions: JEE Main 2011 Mathematics 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 $R$.