If the universal set is \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\), and \(B=\{5,6,7,8\}\), what is \((A\cup B)^c\)?
Answer and explanation
Correct answer: \(\varnothing\)
The union combines all elements of the two sets: \(A\cup B=\{1,2,3,4,5,6,7,8\}=U\). The complement of a set consists of elements of U that are outside that set. Since the union already equals all of U, there are no elements left outside it. Consequently, \((A\cup B)^c=U^c=\varnothing\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
The union combines all elements of the two sets: \(A\cup B=\{1,2,3,4,5,6,7,8\}=U\). The complement of a set consists of elements of U that are outside that set. Since the union already equals all of U, there are no elements left outside it. Consequently, \((A\cup B)^c=U^c=\varnothing\), making option A 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.
