If U = {1, 2, 3, 4, 5, 6} and Aᶜ = {5, 6}, what is A?
Answer and explanation
Correct answer: {1, 2, 3, 4}
The complement Aᶜ consists of the elements of the universal set U that are not in A. Therefore, A contains all elements of U that are not listed in Aᶜ. Removing 5 and 6 from U gives A = U − Aᶜ = {1, 2, 3, 4, 5, 6} − {5, 6} = {1, 2, 3, 4}. Thus option A is correct. Option B is the given complement, option C incorrectly includes elements of Aᶜ, and option D would be possible only if Aᶜ were equal to U.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 4}
Why is this the correct answer?
The complement Aᶜ consists of the elements of the universal set U that are not in A. Therefore, A contains all elements of U that are not listed in Aᶜ. Removing 5 and 6 from U gives A = U − Aᶜ = {1, 2, 3, 4, 5, 6} − {5, 6} = {1, 2, 3, 4}. Thus option A is correct. Option B is the given complement, option C incorrectly includes elements of Aᶜ, and option D would be possible only if Aᶜ were equal to U.
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.
