Consider the following relations :-

Question:

Consider the following relations :-

$\mathrm{R}=\{(\mathrm{x}, \mathrm{y}) \mid \mathrm{x}, \mathrm{y}$ are real numbers and $\mathrm{x}=$ wy for some rational number $\mathrm{w}\}$;

$\mathrm{S}=\left\{\left(\frac{\mathrm{m}}{\mathrm{n}}, \frac{\mathrm{p}}{\mathrm{q}}\right) \mid \mathrm{m}, \mathrm{n}, \mathrm{p}\right.$ and $\mathrm{q}$ are integers such that $\mathrm{n}, \mathrm{q} \neq 0$ and $\left.\mathrm{qm}=\mathrm{pn}\right\}$

Then :

 

  1. $\mathrm{R}$ is an equivalence relation but $\mathrm{S}$ is not an equivalence relation

  2. Neither $\mathrm{R}$ nor $\mathrm{S}$ is an equivalence relation

  3. $\mathrm{S}$ is an equivalence relation but $\mathrm{R}$ is not an equivalence relation

  4. $\mathrm{R}$ and $\mathrm{S}$ both are equivalence relations.


Correct Option: , 3

Solution:

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