If U = {1, 2, ..., 18}, A = {2, 4, 6, 8, 10, 12, 14, 16, 18}, and B = {1, 2, 3, 5, 8, 13}, what is A′ ∩ B′?
Answer and explanation
Correct answer: {7, 9, 11, 15, 17}
Relative to U, A contains every even number, so A′ is the odd-number set {1, 3, 5, 7, 9, 11, 13, 15, 17}. To obtain A′ ∩ B′, remove from A′ every member that occurs in B. The odd members of B are 1, 3, 5, and 13. Removing them leaves {7, 9, 11, 15, 17}. Therefore option A is correct; option B is simply A′, and option C is A ∩ B.
Frequently asked questions
What is the correct answer to this question?
{7, 9, 11, 15, 17}
Why is this the correct answer?
Relative to U, A contains every even number, so A′ is the odd-number set {1, 3, 5, 7, 9, 11, 13, 15, 17}. To obtain A′ ∩ B′, remove from A′ every member that occurs in B. The odd members of B are 1, 3, 5, and 13. Removing them leaves {7, 9, 11, 15, 17}. Therefore option A is correct; option B is simply A′, and option C is 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.
