If H₁ = {x : x ∈ ℕ, x is a factor of 16 and x is even}, what type of set is H₁?
Answer and explanation
Correct answer: Finite set
The positive natural-number factors of 16 are 1, 2, 4, 8, and 16. Among them, the even factors are 2, 4, 8, and 16, so H₁ = {2, 4, 8, 16}. This set has exactly four elements. Because the factors are selected from a fixed number and the list ends, H₁ is a finite set. It is not empty, infinite, or equal to all natural numbers.
Frequently asked questions
What is the correct answer to this question?
Finite set
Why is this the correct answer?
The positive natural-number factors of 16 are 1, 2, 4, 8, and 16. Among them, the even factors are 2, 4, 8, and 16, so H₁ = {2, 4, 8, 16}. This set has exactly four elements. Because the factors are selected from a fixed number and the list ends, H₁ is a finite set. It is not empty, infinite, or equal to all natural numbers.
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.
