If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}, what is (A ∪ B) \ B equal to?
Answer and explanation
Correct answer: {1, 2, 3}
The union contains all distinct elements: A ∪ B = {1, 2, 3, 4, 5, 6, 7}. Subtracting B removes 4, 5, 6, and 7 from this union, leaving {1, 2, 3}. This is also the identity (A ∪ B) \ B = A \ B, because all elements of B are removed. Therefore option A is correct; option C gives B \ A instead, while D is the un-subtracted union.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3}
Why is this the correct answer?
The union contains all distinct elements: A ∪ B = {1, 2, 3, 4, 5, 6, 7}. Subtracting B removes 4, 5, 6, and 7 from this union, leaving {1, 2, 3}. This is also the identity (A ∪ B) \ B = A \ B, because all elements of B are removed. Therefore option A is correct; option C gives B \ A instead, while D is the un-subtracted union.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
