If \(A\cap(B\cup C)=(A\cap B)\cup(A\cap C)\), which law is this?
Answer and explanation
Correct answer: Distributive law
The identity \(A\cap(B\cup C)=(A\cap B)\cup(A\cap C)\) states that intersection distributes over union. The operation outside the parentheses, intersection, is applied separately to both terms inside the union. This is different from the commutative law, which merely changes order, and the associative law, which changes grouping. Therefore option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
Distributive law
Why is this the correct answer?
The identity \(A\cap(B\cup C)=(A\cap B)\cup(A\cap C)\) states that intersection distributes over union. The operation outside the parentheses, intersection, is applied separately to both terms inside the union. This is different from the commutative law, which merely changes order, and the associative law, which changes grouping. Therefore option A is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
