If U = {1, 2, …, 20}, A = {1, 4, 9, 16} and B = {3, 6, 9, 12, 15, 18}, what is A ∩ B′?
Answer and explanation
Correct answer: {1, 4, 16}
The complement B′ contains every element of U that is not in B. To form A ∩ B′, retain only those members of A that are absent from B. The set A is {1, 4, 9, 16}; among these, 9 is also in B, so it must be removed. The remaining elements 1, 4, and 16 are in A but not in B, giving A ∩ B′ = {1, 4, 16}. Thus option A is correct; option B is the common part A ∩ B.
Frequently asked questions
What is the correct answer to this question?
{1, 4, 16}
Why is this the correct answer?
The complement B′ contains every element of U that is not in B. To form A ∩ B′, retain only those members of A that are absent from B. The set A is {1, 4, 9, 16}; among these, 9 is also in B, so it must be removed. The remaining elements 1, 4, and 16 are in A but not in B, giving A ∩ B′ = {1, 4, 16}. Thus option A is correct; option B is the common part A ∩ B.
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.
