Which statement is correct for the set D = {x ∈ ℕ : x² = 16}?
Answer and explanation
Correct answer: D = {4}
Solving x² = 16 over the integers gives x = 4 or x = -4. However, the definition restricts x to the natural numbers, and -4 is not a natural number. The only permitted solution is x = 4, since 4² = 16. Consequently, the set contains exactly one element: D = {4}. Option A ignores the natural-number restriction, and options C and D omit the valid solution.
Frequently asked questions
What is the correct answer to this question?
D = {4}
Why is this the correct answer?
Solving x² = 16 over the integers gives x = 4 or x = -4. However, the definition restricts x to the natural numbers, and -4 is not a natural number. The only permitted solution is x = 4, since 4² = 16. Consequently, the set contains exactly one element: D = {4}. Option A ignores the natural-number restriction, and options C and D omit the valid solution.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
