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

Question

( A ) neither S nor T is an equivalence relation on R
( B ) S is an equivalence relation on R but T is not
( C ) T is an equivalence relation on R but S is not
( D ) both S and T are equivalence relations on R