Which law is represented by A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)?
Answer and explanation
Correct answer: Distributive law
The displayed identity shows union distributed over intersection: the set A is combined separately with B and with C, and the resulting expressions are intersected. This is the distributive law of set algebra. The commutative law changes order, the associative law changes grouping, and the idempotent law has the form A ∪ A = A or A ∩ A = A. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
Distributive law
Why is this the correct answer?
The displayed identity shows union distributed over intersection: the set A is combined separately with B and with C, and the resulting expressions are intersected. This is the distributive law of set algebra. The commutative law changes order, the associative law changes grouping, and the idempotent law has the form A ∪ A = A or A ∩ A = A. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
