Let R be the real line. Consider the following subsets of the plane R × 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?
-
neither S nor T is an equivalence relation on R
-
both S and T are equivalence relations on R
-
S is an equivalence relation on R but T is not
-
T is an equivalence relation on R but S is not
