If the universal set is U = ℝ, A = (−3, ∞), and B = (−∞, 5], what is (A ∩ B)'?
Answer and explanation
Correct answer: (−∞, −3] ∪ (5, ∞)
A contains all real numbers greater than −3, while B contains all real numbers less than or equal to 5. Hence, A ∩ B = (−3, 5]. Taking the complement relative to ℝ gives all real numbers at most −3 or greater than 5. Therefore, (A ∩ B)' = (−∞, −3] ∪ (5, ∞). The endpoint −3 is included because it was excluded from the intersection, whereas 5 is excluded because it belonged to the intersection.
Frequently asked questions
What is the correct answer to this question?
(−∞, −3] ∪ (5, ∞)
Why is this the correct answer?
A contains all real numbers greater than −3, while B contains all real numbers less than or equal to 5. Hence, A ∩ B = (−3, 5]. Taking the complement relative to ℝ gives all real numbers at most −3 or greater than 5. Therefore, (A ∩ B)' = (−∞, −3] ∪ (5, ∞). The endpoint −3 is included because it was excluded from the intersection, whereas 5 is excluded because it belonged to the intersection.
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.
