I am attempting the following question:
Let $S = \Bbb Z$ x $(\Bbb Z $ \ $\{0\})$, be pairs of integers where the second coordinate is non-zero. Let the relation $R \subseteq S ^2$ be defined by:
$(a,b)R(c,d) \leftrightarrow ad = bc$
(a) Describe the following properties of relations: reflexive, symmetric and transitive.
(b) Show that $R$ has these properties.
(c) What is the name for relations satisfying the properties in (a).
(d) Is the function $f: R\times R \rightarrow \Bbb Q$ defined by $f(a,b) = > a/b$ bijective?
I know how to decribe the properties of relations, so question (a) shouldn't be an issue.
I believe the answer to question (c) is "an equivalence relation".
However, I am completely lost as to where I start with questions (b) and (d). I have been trying to understand relations for weeks, but just can't seem to wrap my head around it.
Any help explaining (b) and (d) would be greatly appreciated.