Given the universal set \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,3,5,8\}\), what is the value of \((A\cup B)^c\)?
Answer and explanation
Correct answer: \(\{4,6\}\)
First form the union by listing each element that appears in either set: \(A\cup B=\{1,2,3,5,7,8\}\). To find its complement, select the elements of \(U\) that are absent from this union. The only such elements are 4 and 6. Therefore, \((A\cup B)^c=\{4,6\}\), making option A correct. Option C is the intersection \(A\cap B\), not the complement.
Frequently asked questions
What is the correct answer to this question?
\(\{4,6\}\)
Why is this the correct answer?
First form the union by listing each element that appears in either set: \(A\cup B=\{1,2,3,5,7,8\}\). To find its complement, select the elements of \(U\) that are absent from this union. The only such elements are 4 and 6. Therefore, \((A\cup B)^c=\{4,6\}\), making option A correct. Option C is the intersection \(A\cap B\), not the complement.
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.
