Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 5, 6}, and Aᶜ ⊆ B ⊆ U. Which is the smallest possible set B?
Answer and explanation
Correct answer: {7, 8, 9, 10}
The complement of A with respect to U consists of elements in U that are not in A. Since A contains 1 through 6, we get Aᶜ = {7, 8, 9, 10}. The condition Aᶜ ⊆ B requires B to contain all four of these elements, while B may contain additional elements from U. The smallest such B contains no extras, so B = Aᶜ = {7, 8, 9, 10}.
Frequently asked questions
What is the correct answer to this question?
{7, 8, 9, 10}
Why is this the correct answer?
The complement of A with respect to U consists of elements in U that are not in A. Since A contains 1 through 6, we get Aᶜ = {7, 8, 9, 10}. The condition Aᶜ ⊆ B requires B to contain all four of these elements, while B may contain additional elements from U. The smallest such B contains no extras, so B = Aᶜ = {7, 8, 9, 10}.
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.
