# Math Help - equivalence relations

1. ## equivalence relations

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

2. ## 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?

3. ## Re: equivalence relations

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

4. ## Re: equivalence relations

For all a you need that a~a.
What does that mean for your relationship?
What are the possibilities for a?

5. ## Re: equivalence relations

Originally Posted by ILikeSerena

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

6. ## Re: equivalence relations

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 $0>0~?$

7. ## Re: equivalence relations

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