If U = ℝ and A = [0, 4) ∪ (7, 10], what is A′?
Answer and explanation
Correct answer: (-∞, 0) ∪ [4, 7] ∪ (10, ∞)
The complement A′ contains all real numbers that are not in A. Since 0 is included in [0, 4), it is excluded from the complement; 4 is excluded from [0, 4), so 4 is included in A′. Similarly, 7 is excluded from (7, 10], while 10 is included in A. Therefore, A′ = (-∞, 0) ∪ [4, 7] ∪ (10, ∞).
Frequently asked questions
What is the correct answer to this question?
(-∞, 0) ∪ [4, 7] ∪ (10, ∞)
Why is this the correct answer?
The complement A′ contains all real numbers that are not in A. Since 0 is included in [0, 4), it is excluded from the complement; 4 is excluded from [0, 4), so 4 is included in A′. Similarly, 7 is excluded from (7, 10], while 10 is included in A. Therefore, A′ = (-∞, 0) ∪ [4, 7] ∪ (10, ∞).
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.
