Let $R$ be the real line. Let the relations $S$ and $T$ on $R$ be defined by $S=\{(x, y): y=x+1,0 < x < 2\}, T=\{(x, y):(x-y)$ is an integer $\}$. Then

• A

  both $S$ and $T$ are equivalence relations on $R$
• Correct answer
  B

  $\mathrm{T}$ is an equivalence on $\mathrm{R}$ but $\mathrm{S}$ is not
• C

  neither $S$ nor $T$ is an equivalence relation on $R$
• D

  $\mathrm{S}$ is an equivalence relation on $\mathrm{R}$ but $\mathrm{T}$ is not

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