Question

Which of the following is the empty set?

• A. {x : x is a real number and $x^2-1=0$}
• B. {x : x is a real number and $x^2+1=0$}
• C. {x : x is real number and $x^2-9=0$}
• D. {x : x is real number and $x^2=x+2$}

Answer 1

Answer: (B)

{x : x is a real number and $x^2+1=0$}

The set that does not contain any element is called empty set

Option $B$ defines the set of real numbers for $x^2+1=0$

$\Rightarrow x^2=-1\Rightarrow x=\sqrt{-1}=i$

which is an imaginary number but our set is defined on real numbers

So option $B$ is correct