JEE Math Practice Question
Consider the following relations $R=\{(x, y) \mid x, y$ are real numbers and $x=w y$ for some rational number $w\}$; $S=\left\{\left(\frac{m}{n}, \frac{p}{q}\right) \mid m, n, p\right.$ and $q$ are integers such that $n, q \neq 0$ and $q m=p m\}$. Then
- A.$R$ is an equivalence relation but $S$ is not an equivalence relation
- B.Neither $R$ nor $S$ is an equivalence relation
- C.$S$ is an equivalence relation but $R$ is not an equivalence relation
- D.$R$ and $S$ both are equivalence relations
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