If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is (A \ B) ∪ (B \ A)?
Answer and explanation
Correct answer: {1, 2, 5, 6}
The difference A \ B contains elements present in A but absent from B, so A \ B = {1, 2}. Similarly, B \ A contains elements present in B but absent from A, giving B \ A = {5, 6}. Their union is {1, 2} ∪ {5, 6} = {1, 2, 5, 6}. Thus the expression collects the elements belonging to exactly one of the two sets and excludes the common elements 3 and 4.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 5, 6}
Why is this the correct answer?
The difference A \ B contains elements present in A but absent from B, so A \ B = {1, 2}. Similarly, B \ A contains elements present in B but absent from A, giving B \ A = {5, 6}. Their union is {1, 2} ∪ {5, 6} = {1, 2, 5, 6}. Thus the expression collects the elements belonging to exactly one of the two sets and excludes the common elements 3 and 4.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
