# relations

• June 16th 2008, 10:55 AM
robocop_911
relations
R = {(a,b)/ a>b} on the set of positive integers.

Find the smallest relation that is both reflexive and symmetric...

Is it...

R={ (a,b)/ a>=b} or is it wrong?
• June 16th 2008, 11:34 AM
Plato
Quote:

Originally Posted by robocop_911
R = {(a,b)/ a>b} on the set of positive integers. Find the smallest relation that is both reflexive and symmetric...

I have absolutely no idea what "smallest" could possibly mean in this context.
But here is a very simple one: $E = \left\{ {\left( {x,y} \right)|x = y} \right\}$.