If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4}, and Aᶜ ⊆ B, which elements must at least be in B?
Answer and explanation
Correct answer: {5,6,7,8,9,10}
The complement Aᶜ contains every element of the universal set U that is not present in A. Removing 1, 2, 3, and 4 from U gives Aᶜ = {5,6,7,8,9,10}. Since Aᶜ is a subset of B, every one of these six elements must occur in B. B may contain additional elements, but it cannot omit any of them; therefore option B is the required minimum set.
Frequently asked questions
What is the correct answer to this question?
{5,6,7,8,9,10}
Why is this the correct answer?
The complement Aᶜ contains every element of the universal set U that is not present in A. Removing 1, 2, 3, and 4 from U gives Aᶜ = {5,6,7,8,9,10}. Since Aᶜ is a subset of B, every one of these six elements must occur in B. B may contain additional elements, but it cannot omit any of them; therefore option B is the required minimum 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.
