If A = {2, 4} and B = {4, 6, 8}, what is A ∪ (A ∩ B)?
Advertisement
Answer and explanation
Correct answer: {2, 4}
The common elements of A and B are found first: A ∩ B = {4}. Therefore, A ∪ (A ∩ B) = {2, 4} ∪ {4}. A union retains every element from either set, and 4 is already present in A, so no new element is added. The result is {2, 4}. This illustrates the absorption law A ∪ (A ∩ B) = A.
Frequently asked questions
What is the correct answer to this question?
{2, 4}
Why is this the correct answer?
The common elements of A and B are found first: A ∩ B = {4}. Therefore, A ∪ (A ∩ B) = {2, 4} ∪ {4}. A union retains every element from either set, and 4 is already present in A, so no new element is added. The result is {2, 4}. This illustrates the absorption law A ∪ (A ∩ B) = A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
Advertisement