Question

Which of the following is a singleton set?

• A. \( \{ x : x^2 = 4, \, x \in \mathbb{R} \} \)
• B. \( \{ x : |x|<4, \, x \in \mathbb{N} \} \)
• C. \( \{ x : |x|<-4, \, x \in \mathbb{N} \} \)
• D. \( \{ x : x^2 = 4, \, x \in \mathbb{N} \} \)

Hint:

A singleton set contains exactly one element. In this case, the set containing \( x = 2 \) is a singleton set, because the only natural number solution to \( x^2 = 4 \) is 2.

Answer 1

The Correct Option is D

A singleton set is a set that contains exactly one element. - Option A: \( \{ x : x^2 = 4, \, x \in \mathbb{R} \} \) gives two solutions, \( x = 2 \) and \( x = -2 \), so it is not a singleton set. - Option B: \( \{ x : |x|<4, \, x \in \mathbb{N} \} \) includes all natural numbers less than 4, so it contains more than one element. It is not a singleton set. - Option C: \( \{ x : |x|<-4, \, x \in \mathbb{N} \} \) has no solution, because no natural number satisfies \( |x|<-4 \). - Option D: \( \{ x : x^2 = 4, \, x \in \mathbb{N} \} \) gives the solution \( x = 2 \), which is a singleton set. Therefore, the correct answer is option (D)