If D₁ = {x : x ∈ ℕ, x is a factor of both 12 and 18, and x > 6}, what is D₁?
Answer and explanation
Correct answer: D₁ = ∅
The common natural-number factors of 12 and 18 are 1, 2, 3, and 6. The additional condition requires x to be greater than 6, but none of these common factors satisfies that inequality. Hence no element belongs to D₁, and the correct description is D₁ = ∅, the empty set. It is not {6}, because 6 is not greater than 6.
Frequently asked questions
What is the correct answer to this question?
D₁ = ∅
Why is this the correct answer?
The common natural-number factors of 12 and 18 are 1, 2, 3, and 6. The additional condition requires x to be greater than 6, but none of these common factors satisfies that inequality. Hence no element belongs to D₁, and the correct description is D₁ = ∅, the empty set. It is not {6}, because 6 is not greater than 6.
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.
