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)

The set $A = \\{x: x^2 = 2 \,\forall \,x \,\in\, R\\}$

Answer 2

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.