Which law is represented by A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)?
Answer and explanation
Correct answer: Distributive law
The displayed identity is the distributive law of intersection over union. It has the same pattern as algebraic distribution: A is distributed across the union inside the parentheses, producing (A ∩ B) ∪ (A ∩ C). The commutative law changes the order of sets, the associative law changes grouping, and the complement law involves complements such as A′. 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 displayed identity is the distributive law of intersection over union. It has the same pattern as algebraic distribution: A is distributed across the union inside the parentheses, producing (A ∩ B) ∪ (A ∩ C). The commutative law changes the order of sets, the associative law changes grouping, and the complement law involves complements such as A′. 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).
