The set E₁ = {x : x ∈ ℕ, x = 30/n, n ∈ ℕ} is equal to which set?
Answer and explanation
Correct answer: {1, 2, 3, 5, 6, 10, 15, 30}
For x = 30/n to be a natural number, n must be a positive divisor of 30. As n runs through the positive divisors of 30, the quotient values are also exactly the positive divisors of 30: 1, 2, 3, 5, 6, 10, 15, and 30. Therefore, E₁ equals the set in option A. Numbers such as 4 are not included because they do not divide 30.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 5, 6, 10, 15, 30}
Why is this the correct answer?
For x = 30/n to be a natural number, n must be a positive divisor of 30. As n runs through the positive divisors of 30, the quotient values are also exactly the positive divisors of 30: 1, 2, 3, 5, 6, 10, 15, and 30. Therefore, E₁ equals the set in option A. Numbers such as 4 are not included because they do not divide 30.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
