If U = ℝ, A = (1,4] and B = [4,7), what is (A ∪ B)'?
Answer and explanation
Correct answer: (-∞,1] ∪ [7,∞)
The intervals A = (1,4] and B = [4,7) meet at 4, and 4 is included in both sets. Therefore, their union is (1,7): 1 is excluded and 7 is excluded. Since the universal set is ℝ, the complement contains every real number outside this open interval. Hence (A ∪ B)' = (-∞,1] ∪ [7,∞). The endpoints 1 and 7 belong to the complement because they do not belong to A ∪ B.
Frequently asked questions
What is the correct answer to this question?
(-∞,1] ∪ [7,∞)
Why is this the correct answer?
The intervals A = (1,4] and B = [4,7) meet at 4, and 4 is included in both sets. Therefore, their union is (1,7): 1 is excluded and 7 is excluded. Since the universal set is ℝ, the complement contains every real number outside this open interval. Hence (A ∪ B)' = (-∞,1] ∪ [7,∞). The endpoints 1 and 7 belong to the complement because they do not belong to 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.
