If the universal set U = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, and B = {3, 4, 5}, what is (A ∪ B)′?
Answer and explanation
Correct answer: {6}
First form the union by listing every element that belongs to A or B: A ∪ B = {1, 2, 3, 4, 5}. The complement is taken with respect to U, so we select the elements of U that are absent from this union. Only 6 is missing from A ∪ B. Therefore, (A ∪ B)′ = {6}, making option A correct. Option B is the union itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
{6}
Why is this the correct answer?
First form the union by listing every element that belongs to A or B: A ∪ B = {1, 2, 3, 4, 5}. The complement is taken with respect to U, so we select the elements of U that are absent from this union. Only 6 is missing from A ∪ B. Therefore, (A ∪ B)′ = {6}, making option A correct. Option B is the union 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.
