Which of the following are examples of the null set?
Question:

Which of the following are examples of the null set?

$F=\{x: x \in Q, 1<x<2\}$

 

Solution:

Here, $x \in Q$

i.e. x is a rational number

We know that

If $\mathrm{a}$ and $\mathrm{b}$ are two rational numbers, then $\frac{a+b}{2}$ is a rational number between $\mathrm{a}$ and $\mathrm{b}$ such

that $a<\frac{a+b}{2}<b$

So, the rational number 1 and 2 is

$\frac{1+2}{2}=\frac{3}{2}$

∴ the set is not empty

∴ It is not a null set. 

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