Let $R_1$  be a relation defined in the set of real numbers by $a{R}_{1}b\iff 1+ab>0,$  then $R$   is

 $aRb\iff 1+ab>0$
i) $(a,a)\in R;$    since  $1+a.a=1+a^2>0$
ii)   $(a,b)\in R_1\Rightarrow (b,a)\in R$
$1+ab>0\Rightarrow 1+ba>0$  
So,$R_1$ is reflexive and  symmetric