Let the universal set be \(U=\{1,2,3,\ldots,12\}\), \(A=\{2,3,5,7,11\}\), and \(B=A^c\). What is the value of \(A\cup B\)?
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Answer and explanation
Correct answer: \(U\)
Because \(B=A^c\), set \(B\) contains every element of the universal set that is not in \(A\). Here, \(B=\{1,4,6,8,9,10,12\}\). Together, \(A\) and \(B\) contain every element from 1 through 12, so \(A\cup B=U\). This illustrates the identity \(A\cup A^c=U\).
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 every element of the universal set that is not in \(A\). Here, \(B=\{1,4,6,8,9,10,12\}\). Together, \(A\) and \(B\) contain every element from 1 through 12, so \(A\cup B=U\). This illustrates the identity \(A\cup A^c=U\).
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.
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