Question

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? 

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

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

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

(d) S 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.