Is xy> 0 an equivalence relation? I cant seem to find which property isnt satisfied

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- Apr 22nd 2012, 05:04 AMqwerty31equivalence relations
Is xy> 0 an equivalence relation? I cant seem to find which property isnt satisfied

- Apr 22nd 2012, 05:18 AMILikeSerenaRe: equivalence relations
Let's see...

From wikipedia:

A given binary relation ~ on a set A is said to be an equivalence relation if and only if it is reflexive, symmetric and transitive. Equivalently, for all a, b and c in A:

- a ~ a. (Reflexivity)
- if a ~ b then b ~ a. (Symmetry)
- if a ~ b and b ~ c then a ~ c. (Transitivity)

Did you check these? - Apr 22nd 2012, 05:30 AMqwerty31Re: equivalence relations
- Apr 22nd 2012, 05:39 AMILikeSerenaRe: equivalence relations
Let's start with the first.

For all a you need that a~a.

What does that mean for your relationship?

What are the possibilities for a? - Apr 22nd 2012, 06:34 AMqwerty31Re: equivalence relations
- Apr 22nd 2012, 06:40 AMPlatoRe: equivalence relations
- Apr 22nd 2012, 06:43 AMILikeSerenaRe: equivalence relations