Which of the following expressions is equivalent to \(A\cap(B\cup C)\)?
Answer and explanation
Correct answer: \((A\cap B)\cup(A\cap C)\)
The distributive law for 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 also in at least one of \(B\) or \(C\); this is precisely the condition described by the right side. Option B is the other distributive identity and is not generally equal to the given expression.
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 for 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 also in at least one of \(B\) or \(C\); this is precisely the condition described by the right side. Option B is the other distributive identity and is not generally equal to the given expression.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
