LET ‘ R ’ be the real line . consider the following subsets of the plane R X R . $S\mathit{=}\mathit{\left\{}\mathit{\right(}x\mathit{,}y\mathit{)}\mathit{:}y\mathit{=}x\mathit{+}\mathit{1}\mathit{ }and\mathit{ }o\mathit{<}x\mathit{<}\mathit{2}\mathit{\}} T\mathit{=}\mathit{\left\{}\mathit{\right(}x\mathit{-}y\mathit{)}\mathit{:}x\mathit{-}y$ is an integer} which of the following is true

Given that $R$ is set of all real numbers

Given $S=\left\{\left(x,y\right):y=x+1,0<x<2\right\}$

This is not reflexive, because $\left(1,1\right)$ is not an element in the set $S$

Given $T=\left\{\left(x,y\right): x-y is an integer\right\}$

This is equivalence relation because $\left(x,x\right)\in T$, $\left(x,y\right)\in T\Rightarrow \left(y,x\right)\in T$ and it is transitive also

Therefore, S is not equivalence and T is equivalence relation