Discrete Maths Help

eoins23456

Given the set X={1,2,3,4,5,6,7,8} consider the relation of R on X defined by xRy if 3 divides x-y

(i)=Prove that R is an equivalence relation
(ii)=list the equivalnce classes of R and their elements

So what would be the pairs? is it like the second element minus the first has to be divisible by three or what?
{(1,4),(2,5) ...}

or three has to divide both the elements so just (3,6)?

I know how to show its an equivalence relation but just confused by how to get the pairs.
Any help appreciated!

MathsManiac

It's the first of the two things you mention. So, (1,4),(4,1),(1,7),(7,1),(4,7),(7,4),(1,1),(4,4),(7,7) are all in this relation, as are manyoyer couples. The particular ones I have listed illustrate that one of the equivalence classes is {1,4,7}. This equivalence class could be called "1 bar", written as one with a line over it.

MathsManiac

And, by the way, if your second interpretation had been correct, then it wouldn't be an equivalence relation, since in particular it would not be reflexive, as (1,1) for example would not be in it.

eoins23456

Yeah i was thinking the second one would be wrong as i know ya have to show its reflexive,symmetric and transitive.Thanks!