If \(A\cup(B\cap C)=(A\cup B)\cap(A\cup C)\), which law is this?
Answer and explanation
Correct answer: Distributive law
This identity shows union distributing over intersection: \(A\cup(B\cap C)=(A\cup B)\cap(A\cup C)\). The union with \(A\) is distributed across both members of the intersection. It is not De Morgan’s law because no complements appear, and it is not absorption because neither side reduces simply to \(A\). Thus option A is correct. The two distributive identities should be distinguished by the operation outside the parentheses.
Frequently asked questions
What is the correct answer to this question?
Distributive law
Why is this the correct answer?
This identity shows union distributing over intersection: \(A\cup(B\cap C)=(A\cup B)\cap(A\cup C)\). The union with \(A\) is distributed across both members of the intersection. It is not De Morgan’s law because no complements appear, and it is not absorption because neither side reduces simply to \(A\). Thus option A is correct. The two distributive identities should be distinguished by the operation outside the parentheses.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
