Which identity correctly rewrites \(A\cap(B\cup C)\)?
Answer and explanation
Correct answer: \((A\cap B)\cup(A\cap C)\)
The distributive law of sets states that intersection distributes over union: \(A\cap(B\cup C)=(A\cap B)\cup(A\cap C)\). An element belongs to the left side exactly when it is in \(A\) and in at least one of \(B\) or \(C\). This is precisely the condition represented on the right side. Therefore option A is correct; the other expressions use union, difference, or reversed membership conditions and are not generally equivalent.
Frequently asked questions
What is the correct answer to this question?
\((A\cap B)\cup(A\cap C)\)
Why is this the correct answer?
The distributive law of sets states that intersection distributes over union: \(A\cap(B\cup C)=(A\cap B)\cup(A\cap C)\). An element belongs to the left side exactly when it is in \(A\) and in at least one of \(B\) or \(C\). This is precisely the condition represented on the right side. Therefore option A is correct; the other expressions use union, difference, or reversed membership conditions and are not generally equivalent.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
