If A = {x ∈ N : x is a power of 2 and x ≤ 64}, which set is A equal to?
Answer and explanation
Correct answer: {1, 2, 4, 8, 16, 32, 64}
The powers of 2 not exceeding 64 are obtained from 2⁰ through 2⁶: 2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32, and 2⁶ = 64. Thus A = {1, 2, 4, 8, 16, 32, 64}. The value 1 must be included because 1 = 2⁰, so option B is correct. The set is finite because the condition x ≤ 64 stops the powers.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 4, 8, 16, 32, 64}
Why is this the correct answer?
The powers of 2 not exceeding 64 are obtained from 2⁰ through 2⁶: 2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32, and 2⁶ = 64. Thus A = {1, 2, 4, 8, 16, 32, 64}. The value 1 must be included because 1 = 2⁰, so option B is correct. The set is finite because the condition x ≤ 64 stops the powers.
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.
