If A = {x ∈ ℕ : x is a multiple of 20 and x < 20}, which set is A?
Answer and explanation
Correct answer: Empty set
Under the usual school convention ℕ = {1, 2, 3, ...}, the positive multiples of 20 are 20, 40, 60, and so on. The smallest such multiple is already 20, but the condition requires x < 20. Therefore, no natural number can satisfy both conditions. Hence A contains no elements and is the empty set. Even if a convention includes zero in ℕ, zero is not a positive multiple of 20 in this context.
Frequently asked questions
What is the correct answer to this question?
Empty set
Why is this the correct answer?
Under the usual school convention ℕ = {1, 2, 3, ...}, the positive multiples of 20 are 20, 40, 60, and so on. The smallest such multiple is already 20, but the condition requires x < 20. Therefore, no natural number can satisfy both conditions. Hence A contains no elements and is the empty set. Even if a convention includes zero in ℕ, zero is not a positive multiple of 20 in this context.
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.
