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.