Let $\mathbb{R}$ be the real line. Consider the following subsets of the plane $\mathbb{R}\times \mathbb{R}$:$S=\{(x,y):y=x+1\text{ and }0<x<2\}$$T=\{(x,y):x-y\text{ is an integer}\}$ Which one of the following is true?

1. A
   neither $S$ nor $T$ is an equivalence relation on $\mathbb{R}$
2. B
   both $S$ and $T$ are equivalence relations on $\mathbb{R}$
3. C
   $S$ is an equivalence relation on $\mathbb{R}$ but $T$ is not
4. D
   $T$ is an equivalence relation on $\mathbb{R}$ but $S$ is not