to find the smallest and largest number of equivalence relation in a set Let $s$ be a set of $n$ elements. The number of ordered pairs in the largest and smallest equivalence relation on set $s$ are $n^2$ and $n$.
I am able to understand the largest set of equivalence relation, but in case of smallest set of equivalence relation it could be an empty set..so according to me it is 0.
Am I missing something?

Consider an example set, S = (1,2,3)
Equivalence property follows, reflexive, symmetric
and transitive
Largest ordered set are s x s = 
{ (1,1) (1,2) (1,3) (2,1) (2,2) (2,3) (3,1) (3,2) 
(3,3) } which are 9 which equal to 3^2 = n^2
Smallest ordered set are { (1,1) (2,2) ( 3,3)}
which are 3 and equals to n. number of elements.
https://www.geeksforgeeks.org/gate-gate-cs-2007-question-2/
