If A = {x ∈ ℕ : x is divisible by 11 and x < 11}, what is A?
Answer and explanation
Correct answer: A = ∅ (the empty set)
A natural number divisible by 11 must be a positive multiple of 11, such as 11, 22, 33, and so on. The smallest positive multiple is 11 itself, but the condition x < 11 excludes 11 and every larger multiple. Therefore, no natural number satisfies both conditions, so A is the empty set, written as ∅.
Frequently asked questions
What is the correct answer to this question?
A = ∅ (the empty set)
Why is this the correct answer?
A natural number divisible by 11 must be a positive multiple of 11, such as 11, 22, 33, and so on. The smallest positive multiple is 11 itself, but the condition x < 11 excludes 11 and every larger multiple. Therefore, no natural number satisfies both conditions, so A is the empty set, written as ∅.
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.
