Proving that a relation is symmetric

Question

I need to show that $x \sim y$ if $x=2y$. I started off by assuming that $x,y \in R$. Since $x=2y$, $y=x/2$. Since $y \neq 2x$, $\sim$ is not symmetric. Could I approach the problem is this way?

Answer 1

Yes, you are correct. The relation is not symmetric.

Hope this helps. Ask anything if not clear :)

Answer 2

Yes, you can. Note that all you have to do is to find a pair of real numbers $x,y$ such that $x \sim y$ but $y \nsim x$. Take $x = 2, y = 1$.