Which option gives the correct set-builder form of D = {0, 2, 4, 6, 8}?
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Answer and explanation
Correct answer: D = {2n : n ∈ Z, 0 ≤ n ≤ 4}
Every element of D is twice an integer, and the required values of n are 0, 1, 2, 3, and 4. Thus 2n produces 0, 2, 4, 6, and 8 exactly when n ∈ Z and 0 ≤ n ≤ 4. Option B can depend on whether a convention includes zero in N, so option A is the unambiguous form.
Frequently asked questions
What is the correct answer to this question?
D = {2n : n ∈ Z, 0 ≤ n ≤ 4}
Why is this the correct answer?
Every element of D is twice an integer, and the required values of n are 0, 1, 2, 3, and 4. Thus 2n produces 0, 2, 4, 6, and 8 exactly when n ∈ Z and 0 ≤ n ≤ 4. Option B can depend on whether a convention includes zero in N, so option A is the unambiguous form.
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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