If A = {x ∈ N : x is a power of 2}, which statement about A is correct?
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Answer and explanation
Correct answer: A is an infinite set
The powers of 2 are 2¹, 2², 2³, 2⁴, and so on, giving 2, 4, 8, 16, 32, ... . The exponent can be any positive natural number, and there is no greatest exponent. Consequently, new elements continue to appear without end. Therefore, A is infinite and option A is correct.
Frequently asked questions
What is the correct answer to this question?
A is an infinite set
Why is this the correct answer?
The powers of 2 are 2¹, 2², 2³, 2⁴, and so on, giving 2, 4, 8, 16, 32, ... . The exponent can be any positive natural number, and there is no greatest exponent. Consequently, new elements continue to appear without end. Therefore, A is infinite and option A is correct.
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.
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