If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}, and B = {3, 6, 9}, what is (A ∩ B)ᶜ?
Answer and explanation
Correct answer: {1, 2, 3, 4, 5, 7, 8, 9}
The intersection A ∩ B contains elements common to both sets. The only common element is 6, so A ∩ B = {6}. To find its complement relative to U, remove 6 from U. The result is {1, 2, 3, 4, 5, 7, 8, 9}. Therefore option A is correct, while option B gives the intersection before taking its complement.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 4, 5, 7, 8, 9}
Why is this the correct answer?
The intersection A ∩ B contains elements common to both sets. The only common element is 6, so A ∩ B = {6}. To find its complement relative to U, remove 6 from U. The result is {1, 2, 3, 4, 5, 7, 8, 9}. Therefore option A is correct, while option B gives the intersection before taking its 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.
