Assume that N denotes the set of positive natural numbers. If U = {x ∈ N : x < 7} and A = {x ∈ U : x ≤ 3}, what is the complement Aᶜ of A with respect to U?
Answer and explanation
Correct answer: {4, 5, 6}
Because N is the set of positive natural numbers and x < 7, the universal set is U = {1, 2, 3, 4, 5, 6}. The condition x ≤ 3 gives A = {1, 2, 3}. The complement Aᶜ consists of elements in U that do not belong to A. Removing 1, 2, and 3 from U leaves {4, 5, 6}. Therefore, option A is correct. Option B is A itself, while option D is the complete universal set.
Frequently asked questions
What is the correct answer to this question?
{4, 5, 6}
Why is this the correct answer?
Because N is the set of positive natural numbers and x < 7, the universal set is U = {1, 2, 3, 4, 5, 6}. The condition x ≤ 3 gives A = {1, 2, 3}. The complement Aᶜ consists of elements in U that do not belong to A. Removing 1, 2, and 3 from U leaves {4, 5, 6}. Therefore, option A is correct. Option B is A itself, while option D is the complete universal set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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