Question

Which of the following is not an empty set?

• A. Set of natural numbers $< 1$
• B. Natural number between $3$ and $4$
• C. The set of integers between $-2$ and $-3$
• D. The set $A = \{x: x^2 = 2 \,\forall \,x \,\in\, R\}$

Answer 1

Answer: (D)

There is no natural number less than $1$
$\therefore \,$ Option $(a)$ is an empty set.
There is no natural number between $3$ and $4$
$\therefore \,$ Option $(b)$ is an empty set.
Between two consecutive integers, there exist no integer.
So option $(c)$ is an empty set.
Now, $x^{2} = 2\,\forall\,x \in R$
$\Rightarrow x = \pm\sqrt{2}$
$\therefore \, A = \left\{-\sqrt{2}, \sqrt{2}\right\}$, which contain elements.
$\therefore \,$ It is not an empty set.