# equivalence relations

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• Apr 22nd 2012, 04:04 AM
qwerty31
equivalence relations
Is xy> 0 an equivalence relation? I cant seem to find which property isnt satisfied
• Apr 22nd 2012, 04:18 AM
ILikeSerena
Re: 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:
1. a ~ a. (Reflexivity)
2. if a ~ b then b ~ a. (Symmetry)
3. if a ~ b and b ~ c then a ~ c. (Transitivity)

Did you check these?
• Apr 22nd 2012, 04:30 AM
qwerty31
Re: equivalence relations
Quote:

Originally Posted by ILikeSerena
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:
1. a ~ a. (Reflexivity)
2. if a ~ b then b ~ a. (Symmetry)
3. if a ~ b and b ~ c then a ~ c. (Transitivity)

Did you check these?

Yeah, it seems to me that all 3 are satisfied but I think Im missing something
• Apr 22nd 2012, 04:39 AM
ILikeSerena
Re: 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, 05:34 AM
qwerty31
Re: equivalence relations
Quote:

Originally Posted by ILikeSerena
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?

a would either be positive or negative, and aa > 0 regardless of whether the number is positive or negative
• Apr 22nd 2012, 05:40 AM
Plato
Re: equivalence relations
Quote:

Originally Posted by qwerty31
a would either be positive or negative, and aa > 0 regardless of whether the number is positive or negative

HINT: Is \$\displaystyle 0>0~?\$
• Apr 22nd 2012, 05:43 AM
ILikeSerena
Re: equivalence relations
Quote:

Originally Posted by qwerty31
a would either be positive or negative, and aa > 0 regardless of whether the number is positive or negative

What about a=0?