How to prove that R is equivalence relation

[BlackDeath]

Homework Statement

let X = {1,2,3,..,10} define a relation R on X x X by (a,b)R(c,d) if ad=bc. show that R is an equivalence relation on X x X.

Homework Equations

The Attempt at a Solution

I think that the R have to be reflexive (because ad=bc). Eg. one of the subset is (1,1) which satisfy ad=bc, and reflexive. However, I don't know how to prove that R is symmetric, and transitive? thx

 

[Dick]

R is symmetric if (a,b)R(c,d) if and only if (c,d)R(a,b). Write out what both of those conditions mean in terms of your relation. Same idea for transitive.

 

[BlackDeath]

Got it. thanks :D