If A = {x ∈ ℕ : x is divisible by 2 and x is odd}, what is A?
Answer and explanation
Correct answer: ∅
A natural number divisible by 2 is even by definition. An odd number is a natural number that is not divisible by 2. Therefore no natural number can satisfy both conditions simultaneously. Since there are no elements that belong to A, the set has zero elements and is the empty set, written as ∅. Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
A natural number divisible by 2 is even by definition. An odd number is a natural number that is not divisible by 2. Therefore no natural number can satisfy both conditions simultaneously. Since there are no elements that belong to A, the set has zero elements and is the empty set, written as ∅. Thus option A is correct.
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.
