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 a real number and $x^2=x+2$ }

Answer 1

Answer: (B)

First, we define all the four given sets
(a) { $x:x$ is a real number and $x^2-1=0$ } $=\{1,-1\}$
(b) { $x:x$ is a real number and $x^2+1=0\}$ $=\varphi$
(c) { $x:x$ is a real number and $x^2-9=0$ } $=\{3,-3\}$
(d) { $x:x$ is a real number and $x^2=x+2$ } $=\{-1,2\}$
Clearly, (b) is empty set.