If the universal set \(U=\{1,2,\ldots,16\}\), \(A=\{1,2,4,8,16\}\), and \(B=\{3,6,9,12,15\}\), what is the complement of \(A\cup B\) relative to \(U\)?
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Answer and explanation
Correct answer: \(\{5,7,10,11,13,14\}\)
First form the union: \(A\cup B=\{1,2,3,4,6,8,9,12,15,16\}\). The complement relative to \(U\) contains every element of \(U\) that does not occur in this union. Checking the integers from 1 to 16 leaves \(5,7,10,11,13,14\). Therefore, \((A\cup B)'=\{5,7,10,11,13,14\}\), which is option A.
Frequently asked questions
What is the correct answer to this question?
\(\{5,7,10,11,13,14\}\)
Why is this the correct answer?
First form the union: \(A\cup B=\{1,2,3,4,6,8,9,12,15,16\}\). The complement relative to \(U\) contains every element of \(U\) that does not occur in this union. Checking the integers from 1 to 16 leaves \(5,7,10,11,13,14\). Therefore, \((A\cup B)'=\{5,7,10,11,13,14\}\), which is option A.
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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