Let $R$ be a relation on $N\times N$ defined by$(a,b) R(c,d)$ if and only if$ad (b -c) = bc(a - d )$. Then $R$ is 

$(a,b)R(c,d)\iff ad(b-c)=bc(a-d)$

For reflexive:
$(a,b)R(a,b)\Rightarrow ab(b-a)=ba(a-b)$
$\therefore$ not reflexive
$\begin{array}{r}(a,b)R(c,d)\Rightarrow ad(b-c)=bc(a-d)\\ (c,d)R(a,b)\Rightarrow cb(d-a)=da(c-b)-\text{ true }\end{array}$
$\therefore$symmetric $(2,3)R(3,2)\text{ and }(3,2)R(5,30)\text{ but }(2,3),(5,30)\notin R\Rightarrow$not transitive