Question

Let R be the real line. Consider the following subsets of the plane R × R :

• = {(x, y) : y = x + 1 and 0 < x < 2}

T = {(x, y) : x – y is an integer}.

Which one of the following is true?

(a) T is an equivalence relation on R but * is not

(b) Neither * nor T is an equivalence relation on R

(c) Both * and T are equivalence relations on R

(d) * is an equivalence relation on R but T is not

Answer 1

(a) : To be an equivalence relation the relation must be all – reflexive, symmetric and transitive.