Which is the roster form of U₁ = {x : x ∈ ℕ and 20/x is also a natural number}?
Answer and explanation
Correct answer: U₁ = {1, 2, 4, 5, 10, 20}
For 20/x to be a natural number, x must divide 20 exactly. The positive divisors of 20 are 1, 2, 4, 5, 10, and 20. Each of these values makes 20/x a natural number, whereas 3 does not divide 20 and values such as 40 give a non-natural fraction. Hence the roster form is U₁ = {1, 2, 4, 5, 10, 20}.
Frequently asked questions
What is the correct answer to this question?
U₁ = {1, 2, 4, 5, 10, 20}
Why is this the correct answer?
For 20/x to be a natural number, x must divide 20 exactly. The positive divisors of 20 are 1, 2, 4, 5, 10, and 20. Each of these values makes 20/x a natural number, whereas 3 does not divide 20 and values such as 40 give a non-natural fraction. Hence the roster form is U₁ = {1, 2, 4, 5, 10, 20}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
