If the universal set is \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,3,5,7,9\}\), and \(B=A^c\), what is the value of \(A\cup B\)?
Answer and explanation
Correct answer: \(U\)
Because \(B=A^c\), set \(B\) contains exactly those elements of the universal set that are not in \(A\). Here, \(B=\{2,4,6,8,10\}\). Combining \(A\) and \(B\) includes every element from 1 through 10, so \(A\cup B=U\). This is the complement law: a set and its complement together cover the whole universal set.
Frequently asked questions
What is the correct answer to this question?
\(U\)
Why is this the correct answer?
Because \(B=A^c\), set \(B\) contains exactly those elements of the universal set that are not in \(A\). Here, \(B=\{2,4,6,8,10\}\). Combining \(A\) and \(B\) includes every element from 1 through 10, so \(A\cup B=U\). This is the complement law: a set and its complement together cover the whole universal set.
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.
