If \(U=\{a,b,c,d,e,f\}\), \(A=\{a,c,e\}\), and \(B=\{b,c,f\}\), what is \(A'\cap B'\)?
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Answer and explanation
Correct answer: \(\{d\}\)
Complements are taken relative to U. Thus \(A'=\{b,d,f\}\) and \(B'=\{a,d,e\}\). Their only common element is d, so \(A'\cap B'=\{d\}\). Equivalently, De Morgan’s law gives \(A'\cap B'=(A\cup B)'\); since \(A\cup B=\{a,b,c,e,f\}\), the only element of U outside the union is d.
Frequently asked questions
What is the correct answer to this question?
\(\{d\}\)
Why is this the correct answer?
Complements are taken relative to U. Thus \(A'=\{b,d,f\}\) and \(B'=\{a,d,e\}\). Their only common element is d, so \(A'\cap B'=\{d\}\). Equivalently, De Morgan’s law gives \(A'\cap B'=(A\cup B)'\); since \(A\cup B=\{a,b,c,e,f\}\), the only element of U outside the union is d.
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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