Let the universal set be \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,3,5,8\}\). What is the value of \((A-B)^c\)?
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Answer and explanation
Correct answer: \(\{2,3,4,5,6,8\}\)
The difference \(A-B\) contains elements of \(A\) that do not belong to \(B\). Since 1 and 7 are absent from \(B\), while 3 and 5 occur in \(B\), \(A-B=\{1,7\}\). Taking the complement relative to \(U\) removes 1 and 7 from \(U\), leaving \((A-B)^c=\{2,3,4,5,6,8\}\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{2,3,4,5,6,8\}\)
Why is this the correct answer?
The difference \(A-B\) contains elements of \(A\) that do not belong to \(B\). Since 1 and 7 are absent from \(B\), while 3 and 5 occur in \(B\), \(A-B=\{1,7\}\). Taking the complement relative to \(U\) removes 1 and 7 from \(U\), leaving \((A-B)^c=\{2,3,4,5,6,8\}\). Hence option A is correct.
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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