Question

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 $R$
• B. $T$ is an equivalence on $R$ but $S$ is not
• C. neither $S$ nor $T$ is an equivalence relation on $R$
• D. $S$ is an equivalence relation on $R$ but $T$ is not

Answer 1

Answer: (B)

$T$ is an equivalence but $S$ is not