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)

(Itwasntme)

thanks

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- Aug 19th 2009, 08:21 PMquah13579Discrete 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)

(Itwasntme)

thanks - Aug 19th 2009, 08:45 PMGammanot sure what your sets P are, but...
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

- Aug 25th 2009, 12:36 AMyoonsi
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 =] - Aug 25th 2009, 01:35 AMquah13579
- Aug 25th 2009, 03:09 AMDefunkt
- Aug 27th 2009, 12:17 AMyoonsi
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? (Bow) - Aug 27th 2009, 01:40 AMHallsofIvy