# Math Help - necessity of reflexivity in equivalence relation

1. ## necessity of reflexivity in equivalence relation

I somehow am messed up while reading the conditions that define equivalence relation..by symmetry property x~y implies y~x and by transitivity x~y , y~x implies x~x..so why do we need reflexivity ?

2. ## Re: necessity of reflexivity in equivalence relation

Originally Posted by clerk
I somehow am messed up while reading the conditions that define equivalence relation..by symmetry property x~y implies y~x and by transitivity x~y , y~x implies x~x..so why do we need reflexivity ?
Because it is possible to have a relation on a set which is symmetric and transitive and not be reflexive.
Some element could be missing from any pair in that relation.
$\{a,s,d\}$ and $\{(a,a),(s,s),(a,s),(s,a)\}$ for example.

thanks.