Which set is equal to {2, 4, 8, 16}?
Answer and explanation
Correct answer: {x : x = 2ⁿ, n ∈ ℕ, 1 ≤ n ≤ 4}
For option A, substitute the allowed natural-number exponents n = 1, 2, 3, and 4. The resulting values are 2¹ = 2, 2² = 4, 2³ = 8, and 2⁴ = 16. Thus option A produces exactly the four elements of the given set. Option B gives 2, 4, 6, 8, option C gives 4, 8, 12, 16, and option D omits 16 and includes 1.
Frequently asked questions
What is the correct answer to this question?
{x : x = 2ⁿ, n ∈ ℕ, 1 ≤ n ≤ 4}
Why is this the correct answer?
For option A, substitute the allowed natural-number exponents n = 1, 2, 3, and 4. The resulting values are 2¹ = 2, 2² = 4, 2³ = 8, and 2⁴ = 16. Thus option A produces exactly the four elements of the given set. Option B gives 2, 4, 6, 8, option C gives 4, 8, 12, 16, and option D omits 16 and includes 1.
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.
