# set relations

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• March 4th 2010, 01:03 PM
intervade
set relations
Alright, here is problem, and I'm not really sure whats going on. Ha.

Let A = {1... 10}, Define a relation R on A x A by (x,y)R(q,p) if ad=cb, show that R is an equivalence relation on A x A. Help would be much appreciated!
• March 4th 2010, 01:23 PM
Plato
Please review and correct.
• March 4th 2010, 02:12 PM
intervade
Sorry, what I get for doing more than one problem at a time...

Alright, here is problem, and I'm not really sure whats going on. Ha.

Let A = {1... 10}, Define a relation R on A x A by (x,y)R(q,p) if zp=qy, show that R is an equivalence relation on A x A. Help would be much appreciated!
• March 4th 2010, 03:14 PM
Plato
Well then is it true that $(a,b)\mathcal{R}(a,b),~\forall (a,b)\in A\times A?$
If $(a,b)\mathcal{R}(c,d)$ then is it true that $(c,d)\mathcal{R}(a,b)?$
If $(a,b)\mathcal{R}(c,d)~\&~ (c,d)\mathcal{R}(e,f)$ then is it true that $(a,b)\mathcal{R}(e,f)?$