The given set is the example of an empty set or not? x : x^2- 2 =… - Vidyadip

Question

The given set is the example of an empty set or not$?$
$\{x : x^2- 2 = 0$ and x is rational$\}$

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Answer

$\{\text{x}^2-2=0\Rightarrow\text{x}^2=2\Rightarrow\text{x}=\pm\sqrt{2}\in\text{Q}\},$ the set of rational numbers So, this set is empty.

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