If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} and A = {3, 6, 9, 12}, what is the complement Aᶜ of A with respect to U?
Answer and explanation
Correct answer: {1, 2, 4, 5, 7, 8, 10, 11}
The complement Aᶜ contains every element of the universal set U that is not an element of A. Starting with U, remove 3, 6, 9, and 12. The elements left are 1, 2, 4, 5, 7, 8, 10, and 11, so option A is correct. Option B repeats A rather than giving its complement; options C and D contain elements of A and therefore cannot be the required complement.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 4, 5, 7, 8, 10, 11}
Why is this the correct answer?
The complement Aᶜ contains every element of the universal set U that is not an element of A. Starting with U, remove 3, 6, 9, and 12. The elements left are 1, 2, 4, 5, 7, 8, 10, and 11, so option A is correct. Option B repeats A rather than giving its complement; options C and D contain elements of A and therefore cannot be the required 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.
