Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Define A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Which of the following represents the set (A \ B) ∪ (B \ A)?
Show the answer and explanation
Correct answer
A. {1, 2, 5, 6}
Principle or equation
The set difference A \ B contains elements in A but not in B. The union of (A \ B) and (B \ A) is the symmetric difference, containing elements that are in exactly one of A or B.
Why this answer is correct
A \ B = {1, 2} because 3 and 4 are in B. B \ A = {5, 6} because 3 and 4 are in A. Their union is {1, 2, 5, 6}.
Example
If A = {1, 2} and B = {2, 3}, then A \ B = {1} and B \ A = {3}, so the union is {1, 3}.
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