# necessity of reflexivity in equivalence relation

• April 8th 2012, 06:32 AM
clerk
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 ?
• April 8th 2012, 06:44 AM
Plato
Re: necessity of reflexivity in equivalence relation
Quote:

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.
• April 8th 2012, 10:42 PM
clerk
Re: necessity of reflexivity in equivalence relation
thanks.