If A − B = {1, 5}, B − A = {7}, and A ∩ B = {2, 3}, what is A ∪ B?
Answer and explanation
Correct answer: {1, 2, 3, 5, 7}
The union A ∪ B consists of three mutually separate regions: elements in A but not B, elements in B but not A, and elements common to both sets. These are respectively A − B = {1, 5}, B − A = {7}, and A ∩ B = {2, 3}. Combining all distinct elements gives A ∪ B = {1, 2, 3, 5, 7}. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3, 5, 7}
Why is this the correct answer?
The union A ∪ B consists of three mutually separate regions: elements in A but not B, elements in B but not A, and elements common to both sets. These are respectively A − B = {1, 5}, B − A = {7}, and A ∩ B = {2, 3}. Combining all distinct elements gives A ∪ B = {1, 2, 3, 5, 7}. 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).
