If U = R and A = (−∞,−4] ∪ (3,∞), what is A′?
Answer and explanation
Correct answer: (−4,3]
The set A contains every real number less than or equal to −4, and every real number greater than 3. Therefore, the numbers not in A lie between −4 and 3. Because −4 is already included in A, it must be excluded from the complement. Because 3 is not included in A, it must be included in the complement. Hence A′ = (−4,3].
Frequently asked questions
What is the correct answer to this question?
(−4,3]
Why is this the correct answer?
The set A contains every real number less than or equal to −4, and every real number greater than 3. Therefore, the numbers not in A lie between −4 and 3. Because −4 is already included in A, it must be excluded from the complement. Because 3 is not included in A, it must be included in the complement. Hence A′ = (−4,3].
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.
