The number of non-empty equivalence relations on the set {1,2,3} is :

Let R be the required relation  
A = {(1, 1) (2, 2), (3, 3)} 
(i) | R | = 3, when R = A 
(ii) | R | = 5, e.g. R = A  {(1, 2), (2, 1)} 
Number of R can be [3] 
(iii) R = {1, 2, 3} × {1, 2, 3}