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Reviewed CSCA Mathematics question · Hard

Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8}. Define A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Which of the following sets represents the symmetric difference A Δ B, i.e., (A \ B) ∪ (B \ A)?

  1. {1, 2, 5, 6}
  2. {3, 4}
  3. {1, 2, 3, 4, 5, 6}
  4. {7, 8}
Show the answer and explanation

Correct answer

A. {1, 2, 5, 6}

Principle or equation

The symmetric difference of two sets A and B is the set of elements that belong to exactly one of the sets, i.e., (A \ B) ∪ (B \ A).

Why this answer is correct

A \ B = {1, 2} because 3 and 4 are in both. B \ A = {5, 6} because 3 and 4 are in both. Union gives {1, 2, 5, 6}.

Example

If A = {1, 2} and B = {2, 3}, then A Δ B = {1, 3}.

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