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Reviewed CSCA Mathematics question · Easy

Let U = {1, 2, 3, 4, 5, 6, 7, 8} be the universal set. Let A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. What is the set (A ∩ B) ∪ (A \ B)?

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

Correct answer

A. {1, 2, 3, 4}

Principle or equation

The intersection A ∩ B contains elements common to both sets. The set difference A \ B contains elements in A but not in B. The union combines all elements from both results.

Why this answer is correct

A ∩ B = {3, 4}. A \ B = {1, 2}. Their union is {1, 2, 3, 4}.

Example

If A = {a, b, c} and B = {b, c, d}, then A ∩ B = {b, c}, A \ B = {a}, so (A ∩ B) ∪ (A \ B) = {a, b, c}.

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