If \(A\cap B=A\cap C\) and \(A'\cap B=A'\cap C\), what is the correct conclusion about \(B\) and \(C\)?
Answer and explanation
Correct answer: \(B=C\)
The sets A and A' partition the universal set: every element belongs to exactly one of them. Consequently, \(B=(A\cap B)\cup(A'\cap B)\), and similarly \(C=(A\cap C)\cup(A'\cap C)\). The two given equalities make the corresponding parts equal, so their unions are equal. Therefore, \(B=C\), and option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(B=C\)
Why is this the correct answer?
The sets A and A' partition the universal set: every element belongs to exactly one of them. Consequently, \(B=(A\cap B)\cup(A'\cap B)\), and similarly \(C=(A\cap C)\cup(A'\cap C)\). The two given equalities make the corresponding parts equal, so their unions are equal. Therefore, \(B=C\), and 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.
