Which set is equal to {1, 4, 9, 16}?
Answer and explanation
Correct answer: {x² : x ∈ N, 1 ≤ x ≤ 4} = {1, 4, 9, 16}
The natural numbers satisfying 1 ≤ x ≤ 4 are 1, 2, 3, and 4. Squaring these values gives 1² = 1, 2² = 4, 3² = 9, and 4² = 16. Therefore, the set described by {x² : x ∈ N, 1 ≤ x ≤ 4} contains exactly the four elements {1, 4, 9, 16}, so option A is equal to the given set. The other options either contain unsquared numbers, include an extra element such as 0, or contain many more elements.
Frequently asked questions
What is the correct answer to this question?
{x² : x ∈ N, 1 ≤ x ≤ 4} = {1, 4, 9, 16}
Why is this the correct answer?
The natural numbers satisfying 1 ≤ x ≤ 4 are 1, 2, 3, and 4. Squaring these values gives 1² = 1, 2² = 4, 3² = 9, and 4² = 16. Therefore, the set described by {x² : x ∈ N, 1 ≤ x ≤ 4} contains exactly the four elements {1, 4, 9, 16}, so option A is equal to the given set. The other options either contain unsquared numbers, include an extra element such as 0, or contain many more elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
