Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set. Let A be the set of prime numbers in U, and let B be the set of numbers in U that are greater than 6. Which of the following sets is equal to A ∩ B' (the intersection of A with the complement of B)?
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Correct answer
A. {2, 3, 5}
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 A and also in B'.
Why this answer is correct
B = {7, 8, 9, 10}, so B' = {1, 2, 3, 4, 5, 6}. A = {2, 3, 5, 7}. The common elements are {2, 3, 5}.
Example
If U = {1,2,3,4,5}, A = {2,3}, B = {3,4}, then B' = {1,2,5}, so A ∩ B' = {2}.
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