Which of the properties reflexive, symmetric, anti-symmetric and transitive have the relations $R$, $S$, and $T$ below?
a) $X$ is the set of all functions $f: \mathbb{R} \setminus \{0\} \to \mathbb{R} \setminus \{0\}$, and $f \sim_R g$ if $\frac{f}{g}$ is an odd function.
I have been stuck on this question for a day now, it is not even the question I am finding hard to answer, I just simply don't understand what they mean here. Can someone give me something to go on. Like what is meant by $\mathbb{R} \setminus \{0\} \to \mathbb{R} \setminus \{0\}$, what does $\setminus$ represent in this case?