Which statement is correct about the set N = {x ∈ ℕ : x + 3 = 3}, assuming ℕ = {1, 2, 3, ...}?
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Answer and explanation
Correct answer: It is ∅
Solving x + 3 = 3 gives x = 0. However, the question restricts x to the natural numbers ℕ = {1, 2, 3, ...}, which does not contain 0. Therefore no permitted natural number satisfies the equation, so the set has no elements and is the empty set, written as ∅. Option C is correct.
Frequently asked questions
What is the correct answer to this question?
It is ∅
Why is this the correct answer?
Solving x + 3 = 3 gives x = 0. However, the question restricts x to the natural numbers ℕ = {1, 2, 3, ...}, which does not contain 0. Therefore no permitted natural number satisfies the equation, so the set has no elements and is the empty set, written as ∅. Option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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