Question

Which of the following is a null 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 a real number and $x^2-9=0\}$
• D. $\{x:x$ is a real number and $x^2=5x+6\}$

Answer 1

The correct option is B $\{x:x$ is a real number and $x^2+1=0\}$

Option $\left(a\right)$
$x^2-1=0\Rightarrow x=\pm 1$

Option $\left(b\right)$
$x^2+1=0$ has no real solutions
So, It is null set

Option $\left(c\right)$
$x^2-9=0\Rightarrow x=\pm 3$

Option $\left(d\right)$
$x^2-5x-6=0\Rightarrow x=6,-1$