If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and A = {4, 8, 12}, what is the complement Aᶜ with respect to U?
Answer and explanation
Correct answer: {1, 2, 3, 5, 6, 7, 9, 10, 11}
The complement of A contains every element of the universal set U that is not an element of A. Starting with U, remove 4, 8, and 12, because these are the elements of A. The elements left are 1, 2, 3, 5, 6, 7, 9, 10, and 11. Therefore, Aᶜ = U − A = {1, 2, 3, 5, 6, 7, 9, 10, 11}, so option A is correct. The universal set must always be used as the boundary for a complement.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 5, 6, 7, 9, 10, 11}
Why is this the correct answer?
The complement of A contains every element of the universal set U that is not an element of A. Starting with U, remove 4, 8, and 12, because these are the elements of A. The elements left are 1, 2, 3, 5, 6, 7, 9, 10, and 11. Therefore, Aᶜ = U − A = {1, 2, 3, 5, 6, 7, 9, 10, 11}, so option A is correct. The universal set must always be used as the boundary for a complement.
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.
