If U = R, A = [−7, −1), and B = (−3, 5], what is (A ∩ B)′?
Answer and explanation
Correct answer: (−∞, −3] ∪ [−1, ∞)
The intersection must contain numbers common to both intervals. A extends from −7 inclusive to −1 exclusive, while B extends from −3 exclusive to 5 inclusive. Therefore A ∩ B = (−3, −1); neither endpoint is included because −3 is excluded from B and −1 is excluded from A. The complement of this open interval in R includes both endpoints, giving (−∞, −3] ∪ [−1, ∞).
Frequently asked questions
What is the correct answer to this question?
(−∞, −3] ∪ [−1, ∞)
Why is this the correct answer?
The intersection must contain numbers common to both intervals. A extends from −7 inclusive to −1 exclusive, while B extends from −3 exclusive to 5 inclusive. Therefore A ∩ B = (−3, −1); neither endpoint is included because −3 is excluded from B and −1 is excluded from A. The complement of this open interval in R includes both endpoints, giving (−∞, −3] ∪ [−1, ∞).
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.
