Is a dividing relation on the natural numbers an symmetric/antisymmetric relation?

Question

Let $R = \{(x,y) \in (\mathbb{N}\times\mathbb{N}): x \mid 2y\}$. I.e. $R$ is the set of all pairs $(x,y)$ of natural numbers (excluding $0$) such that $x$ divides $2y$.

Is such a relation antisymmetric? Is such a relation symmetric? I can't even find $x$, $y$ such that $(x,y)\in R\land (y,x)\in R$.

Answer 1

Hint: $1 \mid (2 \cdot 2)$ and $2 \mid (2 \cdot 1)$

Answer 2

Consider $x=2$ and $y=4.$ We have that $x\mid 2y$ and $y\mid 2x.$ But $x\ne y.$