If U = ℝ and A = (−∞, −4] ∪ (2, 6), what is A′, the complement of A in ℝ?
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Answer and explanation
Correct answer: (−4, 2] ∪ [6, ∞)
The first part of A contains all real numbers up to and including −4, so the complement begins just after −4; therefore −4 is excluded. The second part contains numbers strictly between 2 and 6, so both 2 and 6 are excluded from A and included in its complement. Hence A′ = (−4, 2] ∪ [6, ∞).
Frequently asked questions
What is the correct answer to this question?
(−4, 2] ∪ [6, ∞)
Why is this the correct answer?
The first part of A contains all real numbers up to and including −4, so the complement begins just after −4; therefore −4 is excluded. The second part contains numbers strictly between 2 and 6, so both 2 and 6 are excluded from A and included in its complement. Hence A′ = (−4, 2] ∪ [6, ∞).
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.
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