Let R be a relation from ℝ (set of real numbers) to   ℝ defined by   R={(a,b)∣a,b∈ℝ and a−b+3 is an irrational number } .  The relation R  is

R={(a,b)∣a,b∈R and a−b+3 is an irrational number }, then R is reflexive since aRa=a−a+3=3 which is an irrational number  3R 1=3−1+3=23−1 which  is an irrational number but    1 R3  =1−3+3=1 which is not irrational number  ∴R is not symmetric  AlsoR is not transitive            (  ∵3R1     and    1R23    but     3R23                                                           ⇒3−23+3=0  ) Hence, R is not an equivalence relation