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 \(\mathrm{S}\) and \(\mathrm{T}\) are equivalence relations on \(\mathrm{R}\)
(B) \(\mathrm{T}\) is an equivalence on \(\mathrm{R}\) but \(\mathrm{S}\) is not
(C) neither \(\mathrm{S}\) nor \(\mathrm{T}\) is an equivalence relation on \(\mathrm{R}\)
(D) \(\mathrm{S}\) is an equivalence relation on \(\mathrm{R}\) but \(\mathrm{T}\) is not
