What type of set is A = {x : x ∈ N, x is a power of 2}?
Answer and explanation
Correct answer: Infinite set
The powers of 2 among the natural numbers include 1, 2, 4, 8, 16, 32, and so on, depending on whether 2⁰ is included. For every nonnegative integer exponent n, 2ⁿ is a natural number, and increasing n gives a new larger value. There is no greatest exponent or last term, so the set is infinite. Option C is correct.
Frequently asked questions
What is the correct answer to this question?
Infinite set
Why is this the correct answer?
The powers of 2 among the natural numbers include 1, 2, 4, 8, 16, 32, and so on, depending on whether 2⁰ is included. For every nonnegative integer exponent n, 2ⁿ is a natural number, and increasing n gives a new larger value. There is no greatest exponent or last term, so the set is infinite. Option C 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.
