If U = R, A = (−∞, 3), and B = [1, ∞), what is (A ∩ B)'?
Answer and explanation
Correct answer: (−∞, 1) ∪ [3, ∞)
The intersection consists of numbers that are at least 1 and less than 3, so A ∩ B = [1, 3). Its complement in R contains numbers less than 1 and numbers greater than or equal to 3. Hence, (A ∩ B)' = (−∞, 1) ∪ [3, ∞), making option A correct. Notice that 1 belongs to the intersection, while 3 does not.
Frequently asked questions
What is the correct answer to this question?
(−∞, 1) ∪ [3, ∞)
Why is this the correct answer?
The intersection consists of numbers that are at least 1 and less than 3, so A ∩ B = [1, 3). Its complement in R contains numbers less than 1 and numbers greater than or equal to 3. Hence, (A ∩ B)' = (−∞, 1) ∪ [3, ∞), making option A correct. Notice that 1 belongs to the intersection, while 3 does not.
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.
