If A △ B = (A \ B) ∪ (B \ A), A = {1, 2, 4, 6}, and B = {2, 3, 4, 5}, what is A △ B?
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Answer and explanation
Correct answer: {1, 3, 5, 6}
The symmetric difference contains elements that belong to exactly one of the two sets. From A, removing the common elements 2 and 4 gives A \ B = {1, 6}. From B, removing 2 and 4 gives B \ A = {3, 5}. Their union is {1, 6} ∪ {3, 5} = {1, 3, 5, 6}. The common elements are deliberately excluded.
Frequently asked questions
What is the correct answer to this question?
{1, 3, 5, 6}
Why is this the correct answer?
The symmetric difference contains elements that belong to exactly one of the two sets. From A, removing the common elements 2 and 4 gives A \ B = {1, 6}. From B, removing 2 and 4 gives B \ A = {3, 5}. Their union is {1, 6} ∪ {3, 5} = {1, 3, 5, 6}. The common elements are deliberately excluded.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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