If the universal set is \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4,5\}\), and \(B=\{6,7,8\}\), what is the value of \((A\cup B)^c\)?
Answer and explanation
Correct answer: \(\varnothing\)
The union combines every element that belongs to either set. Here, \(A\cup B=\{1,2,3,4,5,6,7,8\}=U\), because the two sets together contain all elements of the universal set. Therefore, \((A\cup B)^c=U^c\). The complement of the universal set relative to itself contains no elements, so \(U^c=\varnothing\). Thus, option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
\(\varnothing\)
Why is this the correct answer?
The union combines every element that belongs to either set. Here, \(A\cup B=\{1,2,3,4,5,6,7,8\}=U\), because the two sets together contain all elements of the universal set. Therefore, \((A\cup B)^c=U^c\). The complement of the universal set relative to itself contains no elements, so \(U^c=\varnothing\). Thus, option A is the only correct answer.
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.
