Let $R=\{(x,y): x=y^2\}$ be a relation defined in $\mathbb{Z}$. Is it reflexive, symmetric, transitive or antisymmetric? Let $R=\{(x,y): x=y^2\}$ be a relation defined in $\mathbb{Z}$. Is it reflexive, symmetric, transitive or antisymmetric).
I'm having most trouble determining if this relation is symmetric, how can I tell?

None. $(4,2) \in R, (2,4) \notin R, (2,2) \notin R$. It is anti-symmetric.
