If A = {x : x ∈ N, x is even and x is odd}, what is A?
Answer and explanation
Correct answer: ∅
Every integer, including every natural number, is either even or odd, but no integer can be both even and odd. An even number is divisible by 2, whereas an odd number leaves remainder 1 when divided by 2; these conditions cannot hold simultaneously. Thus no natural number satisfies the defining condition, so A has no elements and A = ∅. Option C is correct.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
Every integer, including every natural number, is either even or odd, but no integer can be both even and odd. An even number is divisible by 2, whereas an odd number leaves remainder 1 when divided by 2; these conditions cannot hold simultaneously. Thus no natural number satisfies the defining condition, so A has no elements and A = ∅. Option C 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.
