Question

How do I prove this is an equivalence relationship?

Answer 1

Is this even an equivalence relationship? It doesn't seem to be reflexive

Answer 2

Btainstorming
a,b are even R = {2,4,6,8,}
R = (a,b) = (a, a +2 )
What is an equivalence relationship?
@mathmate

Answer 3

An equivalence relation is one that is reflexive, symmetric and transitive

Answer 4

Hmm :|

Answer 5

lol this one's easy... had to do a more general form actually. What's your problem with the reflexive property?

Answer 6

Hmm, Is it reflexive/ @inkyvoyd
To me, it doesn't want to seem so since it doesn't have in all ordered pairs from 1 to 9

Answer 7

Are you misunderstanding notation? (a,b) refers to the relation aRb or maybe even a=b if you overload the = operator

Answer 8

Ahh, so that means we are only looking at R and not A?

Answer 9

No, the notation is super confusing. Let me do it another way for the equivalence relation of the equals "=" sign (like 1=1, 1=/=2, etc)
A={1,2,3,4,5,6,7,8,9}
Let R be equivalence relation such that R:={(a,b) | a and b are equal, i.e. a=b}
Does that help illustrate the notation? Of course this is different from the equivalence relation in your problem but I'm just putting it out there to see if it makes things make more sense...

We're simply checking to see if two numbers are the same parity in the original problem. (if both odd, they are equal, if both even, they are equal, if one odd and one even, they are not equal)

Answer 10

Ahh, I get what you're trying to say

Answer 11

yeah so here's a tip - sometimes notation is just trash, but it's part of pure math (and for better or for worse you've found yourself on the doorstep of that domain) to be notation heavy. So I was confused too for this problem, but I just took on faith what they claimed, and tried to make sense of the notation, and that was the result. Of course I googled the usage of ordered pairs to designate equivalence relations, but I had the intuition to do so in the first place by assuming what made the most sense.

Answer 12

Thank you!

Answer 13

did you figure out how to do this?