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. {6, 8}
Principle or equation
Set operations: union (∪) combines elements, intersection (∩) takes common elements, complement (') takes elements in the universal set not in the set.
Why this answer is correct
First find A ∪ B = {1, 2, 3, 4, 5, 6, 8}. The complement of A is A' = {6, 7, 8, 9, 10}. Intersect these two sets: common elements are 6 and 8. So (A ∪ B) ∩ A' = {6, 8}.
Example
If U = {1, 2, 3}, A = {1}, B = {2}, then A ∪ B = {1, 2}, A' = {2, 3}, so (A ∪ B) ∩ A' = {2}.
This published item includes a stored explanation and passed the platform’s publication workflow. It is independent preparation material, not a claim of an official or recalled examination question.