Problem
Let \( A = \{1, 2, 3, 4, 5\} \) and \( B = \{4, 5, 6, 7, 8\} \). Find \( A' \cap B \) and \( B' \cap A \), where \( A' \) and \( B' \) are the complements of sets A and B respectively in the universal set \( U = \{1, 2, 3, 4, 5, 6, 7, 8\} \).
Solution
Step 1 ：First, we find the complements of sets A and B. \( A' = U - A = \{6, 7, 8\} \) and \( B' = U - B = \{1, 2, 3\} \).
Step 2 ：Next, we find the intersection of \( A' \) and \( B \). \( A' \cap B = \{6, 7, 8\} \cap \{4, 5, 6, 7, 8\} = \{6, 7, 8\} \).
Step 3 ：Finally, we find the intersection of \( B' \) and \( A \). \( B' \cap A = \{1, 2, 3\} \cap \{1, 2, 3, 4, 5\} = \{1, 2, 3\} \).
