# Thread: a haunting problem in relations

1. ## a haunting problem in relations

supose p is an equivalent relation
(x,y) E p --> [x]p = [y]p

can anyone pls tell me whether the below approach is correct..

suppose (x,y) E p
let z be arbitrary and suppose
z E [x]p <--> (x,z) E p
<--> .........

like wise by using biconditional arrow, then u dont have to split it into 2 parts,
because i dont see any wrong in it.( since p is equivalent)

2. If $\mathcal{P}$ is an equivalent relation then it is true that
$z\in [{x}]_\mathcal{P}\Leftrightarrow (x,z)\in \mathcal{P}$.