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' ∩ B)?
Show the answer and explanation
Correct answer
B. {2, 4, 6, 8}
Principle or equation
Set operations: intersection (∩), union (∪), complement (A' = U \ A).
Why this answer is correct
A ∩ B = {2, 4}. A' = {6, 7, 8, 9, 10}, so A' ∩ B = {6, 8}. Union gives {2, 4, 6, 8}.
Example
If U = {1,2,3}, A = {1}, B = {2}, then (A∩B) ∪ (A'∩B) = ∅ ∪ {2} = {2}.
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