equivalence relations

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

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?

Quote:

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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?

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Yeah, it seems to me that all 3 are satisfied but I think Im missing something

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?

Quote:

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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?

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

Quote:

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Originally Posted by qwerty31

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

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HINT: Is

Quote:

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Originally Posted by qwerty31

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

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What about a=0?