Question

Which of the following is a singleton set?

• A. $\{x : |x| < 1, x \in I\}$
• B. $\{x: |x| = 5, x \in I\}$
• C. $\{x : x^2= 1, x \in I\}$
• D. $\{x: x^2 + x + 1 = 0, x \in R\}$

Answer 1

Answer: (A)

(a) $\{x : |x| < 1,x \in I\}$
$ = \{x : -1 < x < 1, x \in I\} = \{0\}$
(b) $\{x : |x| = 5, x \in I\}$
$= \{x : x = ± 5\} = \{± 5\}$
(c) $\{x : x^2 = 1, x \in I\}$
$= \{x : x = ± 1\} = \{± 1\}$
(d) $\{x : x^2 + x + 1 = 0, x \in R\}$
$= \left\{x : x = \frac{-1\pm\sqrt{3}i}{2}, x \in R\right\} = \phi$