Thread: Discrete set maths

On the set

define a relation by (x,y)~(u,v) if and only if xv = yu.
(a) Show that ~ is an equivalence relation.
(b) Find the equivalence class of (2,3)


thanks

Im assuming we are in a commutative setting here.
Reflexive
?

Symmetry


Think you can do transitive?

(2,3), so the things equivalent are of the form and must satisfy , so the equivalence class is

I'm sorry but could you explain that again? I'm confused, ab = ba, how does that show that its reflexive? and I thought that (x,y) =/= (y,x)

Thank you =]

Originally Posted by Gamma

Im assuming we are in a commutative setting here.
Reflexive
?

Symmetry


Think you can do transitive?

(2,3), so the things equivalent are of the form and must satisfy , so the equivalence class is

I think p is positive integer.

Originally Posted by yoonsi

I'm sorry but could you explain that again? I'm confused, ab = ba, how does that show that its reflexive? and I thought that (x,y) =/= (y,x)

Thank you =]

~ is reflexive iff

Since is commutative, for any

oh well I understand the concept of reflexivity buuuut, how come P is commutative? I thought in ordered pairs, (2,3) does not equal (3,2)?

Sorry I must seem really silly...

Could someone also step me through showing how that is transitive?

Originally Posted by Gamma

Im assuming we are in a commutative setting here.
Reflexive
?

Symmetry


Think you can do transitive?

(2,3), so the things equivalent are of the form and must satisfy , so the equivalence class is

In other words (a, b) is in the same equivalence class as (2, 3) if and only if . You could think of that class as all fractions that are equivalent to the fraction and so representing the rational number .