If U = R, A = (-3, 4], and B = [1, 6), what is A' ∩ B'?
Answer and explanation
Correct answer: (-∞, -3] ∪ [6, ∞)
Apply De Morgan’s law: A' ∩ B' = (A ∪ B)'. The intervals A = (−3, 4] and B = [1, 6) overlap, so their union is (−3, 6). The endpoint −3 is excluded because A excludes it, and 6 is excluded because B excludes it. The complement in R therefore includes both endpoints: (−∞, −3] ∪ [6, ∞). Hence option A is correct; option B incorrectly excludes the boundary points.
Frequently asked questions
What is the correct answer to this question?
(-∞, -3] ∪ [6, ∞)
Why is this the correct answer?
Apply De Morgan’s law: A' ∩ B' = (A ∪ B)'. The intervals A = (−3, 4] and B = [1, 6) overlap, so their union is (−3, 6). The endpoint −3 is excluded because A excludes it, and 6 is excluded because B excludes it. The complement in R therefore includes both endpoints: (−∞, −3] ∪ [6, ∞). Hence option A is correct; option B incorrectly excludes the boundary points.
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.
