Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 5, 7}, and B = {2, 4, 5, 8, 10}. What is (A ∩ B)′?
Answer and explanation
Correct answer: {1, 3, 4, 6, 7, 8, 9, 10}
First calculate the intersection: A ∩ B = {2, 5}, because 2 and 5 are the only elements common to A and B. The complement of a set is taken with respect to the universal set U, so remove 2 and 5 from U. This gives (A ∩ B)′ = U − {2, 5} = {1, 3, 4, 6, 7, 8, 9, 10}. Option A is the intersection itself, option C is A ∪ B, and option D omits several elements that belong to the complement.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 4, 6, 7, 8, 9, 10}
Why is this the correct answer?
First calculate the intersection: A ∩ B = {2, 5}, because 2 and 5 are the only elements common to A and B. The complement of a set is taken with respect to the universal set U, so remove 2 and 5 from U. This gives (A ∩ B)′ = U − {2, 5} = {1, 3, 4, 6, 7, 8, 9, 10}. Option A is the intersection itself, option C is A ∪ B, and option D omits several elements that belong to the 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.
