If A = {0, 2, 4, 6} and B = {x : x = 2n, n ∈ W, n < 4}, which statement is correct?
Answer and explanation
Correct answer: A = B
The governing idea is translating set-builder notation into roster form and then comparing the resulting elements. Whole numbers are W = {0, 1, 2, 3, ...}. Since n < 4, the possible values are n = 0, 1, 2, 3. Substitution in x = 2n gives x = 0, 2, 4, 6, so B = {0, 2, 4, 6}. This is exactly A; hence A = B. Option C omits 0, and option D contradicts n = 0.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
The governing idea is translating set-builder notation into roster form and then comparing the resulting elements. Whole numbers are W = {0, 1, 2, 3, ...}. Since n < 4, the possible values are n = 0, 1, 2, 3. Substitution in x = 2n gives x = 0, 2, 4, 6, so B = {0, 2, 4, 6}. This is exactly A; hence A = B. Option C omits 0, and option D contradicts n = 0.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
