Consider the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Let A be the set of prime numbers in U, and let B be the set of odd numbers in U. Which of the following sets is equal to A ∩ B' (the intersection of A with the complement of B)?
Show the answer and explanation
Correct answer
A. {2}
Principle or equation
The complement of B (B') consists of all elements in U not in B. The intersection A ∩ B' contains elements that are in both A and B'.
Why this answer is correct
A = {2, 3, 5, 7} (prime numbers in U). B = {1, 3, 5, 7, 9} (odd numbers). B' = {2, 4, 6, 8, 10}. Intersection A ∩ B' = {2}.
Example
If U = {1, 2, 3, 4}, A = {2, 3}, B = {1, 3}, then B' = {2, 4} and A ∩ B' = {2}.
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