If the universal set U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4}, and B = {3, 4, 5}, what is (A ∩ B)ᶜ with respect to U?
Answer and explanation
Correct answer: {1, 2, 5, 6, 7}
First find the intersection: A ∩ B contains elements common to both A and B, so A ∩ B = {3, 4}. To find its complement, select all elements of U that are not in {3, 4}. From U = {1, 2, 3, 4, 5, 6, 7}, the remaining elements are {1, 2, 5, 6, 7}. Thus (A ∩ B)ᶜ = {1, 2, 5, 6, 7}, and option A is correct. Option B gives the intersection itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 5, 6, 7}
Why is this the correct answer?
First find the intersection: A ∩ B contains elements common to both A and B, so A ∩ B = {3, 4}. To find its complement, select all elements of U that are not in {3, 4}. From U = {1, 2, 3, 4, 5, 6, 7}, the remaining elements are {1, 2, 5, 6, 7}. Thus (A ∩ B)ᶜ = {1, 2, 5, 6, 7}, and option A is correct. Option B gives the intersection itself, not 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.
