I'm trying to get my assignment done and I'm finding it hard to understand Relations. The question says:
Let $Q$ be the relation on the set $R$ of non-zero real numbers, where non-zero real numbers $x$ and $y$ satisfy $xQy$ if and only if $x^2/y^2$ is a rational number. Determine:
(i) whether or not the relation $Q$ is reflexive,
(ii) whether or not the relation $Q$ is symmetric,
(iii) whether or not the relation $Q$ is anti-symmetric,
(iv) whether or not the relation $Q$ is transitive,
(v) whether or not the relation $Q$ is a equivalence relation,
(vi) whether or not the relation $Q$ is a partial order.
So far I'm on the 3rd part. I understand that anti-symmetric means when $xQy$ and $yQx$ then $x=y$. This, to me looks a bit like the reflexive relation or maybe I'm wrong.
Thanks in advance.