AIEEE 2010 (Offline)Question 1
Consider the following relations
$R=\{(x,y)\mid x,y\text{ are real numbers and }x=wy\text{ for some rational number }w\}$;
$S=\left\{\left(\frac mn,\frac pq\right)\mid m,n,p\text{ and }q\text{ are integers such that }n,q\neq0\text{ and }qm=pn\right\}$. Then
Sets, Relations and Function
Solution
$R$ is not symmetric: $(0,1)\in R$ ($w=0$) but $1\ne w\cdot0$. $S$ is the relation $\frac mn=\frac pq$, i.e. equality of rationals, which is an equivalence relation.