If A = {5, 6, 7} and B = {6, 7, 8, 9}, what is A ∩ (A ∪ B)?
Answer and explanation
Correct answer: {5, 6, 7}
The union A ∪ B contains every element from either set, so A ∪ B = {5, 6, 7, 8, 9}. Taking the intersection of this union with A selects the elements that are also in A. Since every element of A is already in A ∪ B, the result is A itself: A ∩ (A ∪ B) = {5, 6, 7}. This illustrates the absorption law.
Frequently asked questions
What is the correct answer to this question?
{5, 6, 7}
Why is this the correct answer?
The union A ∪ B contains every element from either set, so A ∪ B = {5, 6, 7, 8, 9}. Taking the intersection of this union with A selects the elements that are also in A. Since every element of A is already in A ∪ B, the result is A itself: A ∩ (A ∪ B) = {5, 6, 7}. This illustrates 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).
