Which expression is equal to A ∩ (B ∪ C)?
Answer and explanation
Correct answer: (A ∩ B) ∪ (A ∩ C)
This is the distributive law of intersection over union: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). An element belongs to the left side when it is in A and also in at least one of B or C. That means it is either in both A and B or in both A and C, which is exactly the right side. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
(A ∩ B) ∪ (A ∩ C)
Why is this the correct answer?
This is the distributive law of intersection over union: A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C). An element belongs to the left side when it is in A and also in at least one of B or C. That means it is either in both A and B or in both A and C, which is exactly the right side. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
