If U = R, A = [-3, 2) and B = (2, 6], what is (A ∪ B)'?
Answer and explanation
Correct answer: (-∞, -3) ∪ {2} ∪ (6, ∞)
The interval A contains every real number from −3 inclusive up to, but not including, 2. The interval B contains numbers greater than 2 up to and including 6. Thus their union leaves exactly the point 2 uncovered between the intervals. Numbers less than −3 and greater than 6 are also outside the union. Hence the complement in R is (−∞, −3) ∪ {2} ∪ (6, ∞), which is option A.
Frequently asked questions
What is the correct answer to this question?
(-∞, -3) ∪ {2} ∪ (6, ∞)
Why is this the correct answer?
The interval A contains every real number from −3 inclusive up to, but not including, 2. The interval B contains numbers greater than 2 up to and including 6. Thus their union leaves exactly the point 2 uncovered between the intervals. Numbers less than −3 and greater than 6 are also outside the union. Hence the complement in R is (−∞, −3) ∪ {2} ∪ (6, ∞), which is option A.
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.
