If \((A\cup B')\cap(A'\cup B')=B'\), which simplification shows it correctly?
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Answer and explanation
Correct answer: \(B'\cup(A\cap A')=B'\)
Apply the distributive law \((X\cup Z)\cap(Y\cup Z)=Z\cup(X\cap Y)\), with \(X=A\), \(Y=A'\), and \(Z=B'\). The expression becomes \(B'\cup(A\cap A')\). A set and its complement are disjoint, so \(A\cap A'=\varnothing\). Therefore the result is \(B'\cup\varnothing=B'\).
Frequently asked questions
What is the correct answer to this question?
\(B'\cup(A\cap A')=B'\)
Why is this the correct answer?
Apply the distributive law \((X\cup Z)\cap(Y\cup Z)=Z\cup(X\cap Y)\), with \(X=A\), \(Y=A'\), and \(Z=B'\). The expression becomes \(B'\cup(A\cap A')\). A set and its complement are disjoint, so \(A\cap A'=\varnothing\). Therefore the result is \(B'\cup\varnothing=B'\).
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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