Let the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}. Which of the following represents the set (A ∪ B) ∩ A?
Show the answer and explanation
Correct answer
A. {1, 2, 3, 4, 5}
Principle or equation
The union of two sets contains all elements that are in either set, and the intersection of two sets contains only elements that are in both sets. Here, A ∪ B = {1, 2, 3, 4, 5, 6, 8}, and intersecting this with A gives exactly the elements of A, since A is a subset of A ∪ B.
Why this answer is correct
First compute A ∪ B = {1, 2, 3, 4, 5} ∪ {2, 4, 6, 8} = {1, 2, 3, 4, 5, 6, 8}. Then (A ∪ B) ∩ A = {1, 2, 3, 4, 5, 6, 8} ∩ {1, 2, 3, 4, 5} = {1, 2, 3, 4, 5}.
Example
If A = {1, 2} and B = {2, 3}, then A ∪ B = {1, 2, 3} and (A ∪ B) ∩ A = {1, 2}.
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