If U=R, A=[1,∞), and B=(−∞,4), what is A′∪B′?
Answer and explanation
Correct answer: (−∞,1)∪[4,∞)
Complements are taken in the real-number universal set. Because A includes 1 and all larger numbers, A′=(−∞,1). Because B contains numbers strictly less than 4 but not 4 itself, B′=[4,∞). Their union is therefore (−∞,1)∪[4,∞). Endpoint brackets are essential: 1 is excluded from A′, while 4 is included in B′.
Frequently asked questions
What is the correct answer to this question?
(−∞,1)∪[4,∞)
Why is this the correct answer?
Complements are taken in the real-number universal set. Because A includes 1 and all larger numbers, A′=(−∞,1). Because B contains numbers strictly less than 4 but not 4 itself, B′=[4,∞). Their union is therefore (−∞,1)∪[4,∞). Endpoint brackets are essential: 1 is excluded from A′, while 4 is included in B′.
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.
