# DM - Functions & Relations -Q16

+1 vote
The number of relations, on a set of five elements, which are both equivalence relation and partial order relation is ______?
reshown 6 days ago

identity relation i.e. $I_A = \{ (a,a) | a \in A \}$
To this relation if we add any one more ordered pair (a,b) where $a \neq b$ , then either symmetric or antisymmetric property will violate. Hence,  the only relation that is both Equivalence relation and Partial order relation is  $I_A = \{ (a,a) | a \in A \}$