A relation R is defined on the set of integers as $ (a, b) \in R $ if and only if $ a^2=b^2 $ then the relation R is
a)an equivalence relation b)a partial ordering c)a total ordering d)None of the mentioned
I thought it as an equivalence relation but it seems wrong.
Reflexive: $(a,a)\in R$
Symmetric: $(a,b)\in R \implies (b,a)\in R$
Transitive: $(a,b)\in R, (b,c)\in R \implies (a,c)\in R$
So it is an equivalence.