# Need help finding the equivalence relation!

"Let A be the set of all people in the world, R a relation on A defined by (a, b) ∈ R, if and only if a is a twin of b. Is this relation an equivalence relation? Explain!"

An equivalence relation is a reflexive, symmetric and transitive relation.

A = set of all people in the world R = {(a,b)| a and b are twins}

Okay so i thought this: This relation is not reflexive (a,a) or (b,b) because I am not my twin. But, it is symmetric because (a,b) and (b,a), that means I am my twin's twin and he/she is also my twin. Transitive in this case would basically mean reflexive, but like I said that is false.

Therefore my relation is not an equivalence relation...

Is my argument correct?

## 1 Answer

Yes, your reasoning is correct.

BTW, with the alternative definition of $$(a, b) ∈ R$$ if and only if $$a$$ is a twin of $$b$$ or $$a$$ and $$b$$ are the same person, the relation $$R$$ becomes an equivalence relation.