If A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ (A ∪ B)?
Answer and explanation
Correct answer: {1, 2, 3}
The union A ∪ B contains every element in either set, so A ∪ B = {1, 2, 3, 4}. Taking the intersection with A selects only elements common to A and this union. Because every element of A is automatically in A ∪ B, the intersection is A itself: A ∩ (A ∪ B) = A = {1, 2, 3}. This is the absorption law.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3}
Why is this the correct answer?
The union A ∪ B contains every element in either set, so A ∪ B = {1, 2, 3, 4}. Taking the intersection with A selects only elements common to A and this union. Because every element of A is automatically in A ∪ B, the intersection is A itself: A ∩ (A ∪ B) = A = {1, 2, 3}. This is the absorption law.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
