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 ?
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.
$\displaystyle \{a,s,d\}$ and $\displaystyle \{(a,a),(s,s),(a,s),(s,a)\}$ for example.