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\} $ $ =\phi $
(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.