If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, and Aᶜ ⊆ B ⊆ U, what is the smallest possible set B?
Answer and explanation
Correct answer: {5, 6, 7, 8, 9}
The complement of A relative to U is obtained by removing the elements of A from U. Therefore, Aᶜ = U − A = {5, 6, 7, 8, 9}. The condition Aᶜ ⊆ B means that B must contain every one of these five elements. To make B as small as possible, we include no additional elements. Thus the minimum choice is B = Aᶜ = {5, 6, 7, 8, 9}, which is option A.
Frequently asked questions
What is the correct answer to this question?
{5, 6, 7, 8, 9}
Why is this the correct answer?
The complement of A relative to U is obtained by removing the elements of A from U. Therefore, Aᶜ = U − A = {5, 6, 7, 8, 9}. The condition Aᶜ ⊆ B means that B must contain every one of these five elements. To make B as small as possible, we include no additional elements. Thus the minimum choice is B = Aᶜ = {5, 6, 7, 8, 9}, which is option A.
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.
