Maths · Sets and their representation
Which of the following is a singleton set?
Which of the following is a singleton set?
- A. \( \{x:|x|=5, x \in N\} \)
- B. \( \{x:|x|=6, x \in Z\} \)
- C. \( \left(x: x^{2}+2 x+1=0, x \in N\right) \)
- D. \( \left\{x: x^{2}=7, x \in N\right\} \)
Step-by-step solution
Option A: x ∈ N (natural numbers) and |x|=5 gives x=5 only, so set is {5}, a singleton. Option B: x ∈ Z gives x=6 and x=-6, two elements. Option C: equation gives x=-1, not in N, empty set. Option D: equation gives x=√7, not in N, empty set. Only A is singleton.