If the universal set is U = R and A = (-∞, -1) ∪ [3, 8), what is A'?
Answer and explanation
Correct answer: [-1, 3) ∪ [8, ∞)
The complement is taken in R. The interval (-∞, -1) excludes -1, so -1 belongs to the complement and the left endpoint is included. The interval [3, 8) includes 3 but excludes 8, so 3 is omitted from the complement while 8 is included. All real numbers from -1 through values less than 3, together with 8 and larger numbers, give A' = [-1, 3) ∪ [8, ∞). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
[-1, 3) ∪ [8, ∞)
Why is this the correct answer?
The complement is taken in R. The interval (-∞, -1) excludes -1, so -1 belongs to the complement and the left endpoint is included. The interval [3, 8) includes 3 but excludes 8, so 3 is omitted from the complement while 8 is included. All real numbers from -1 through values less than 3, together with 8 and larger numbers, give A' = [-1, 3) ∪ [8, ∞). Hence option A is correct.
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.
