If \((A\cap B')\cup(A'\cap B')=B'\), this is an example of which rule?
Answer and explanation
Correct answer: \(B'\cap(A\cup A')=B'\)
Using the distributive law, \((A\cap B')\cup(A'\cap B')\) can be rewritten as \(B'\cap(A\cup A')\). By the complement law, \(A\cup A'=U\), so this becomes \(B'\cap U=B'\), the identity law. Therefore option A correctly states the applicable transformation and resulting equality.
Frequently asked questions
What is the correct answer to this question?
\(B'\cap(A\cup A')=B'\)
Why is this the correct answer?
Using the distributive law, \((A\cap B')\cup(A'\cap B')\) can be rewritten as \(B'\cap(A\cup A')\). By the complement law, \(A\cup A'=U\), so this becomes \(B'\cap U=B'\), the identity law. Therefore option A correctly states the applicable transformation and resulting equality.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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