If U={1,2,3,4,5,6,7,8,9}, A={1,2,5} B={3,6,7} Find A', B' and (A∩B)

Answer

To solve this question, we need to find the complements of sets A and B with respect to the universal set U, as well as their intersection. 1. **Finding A' (the complement of A)**: - Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9} - Set A = {1, 2, 5} - A' consists of all elements in U that are not in A: - A' = U - A = {3, 4, 6, 7, 8, 9}. 2. **Finding B' (the complement of B)**: - Set B = {3, 6, 7} - B' consists of all elements in U that are not in B: - B' = U - B = {1, 2, 4, 5, 8, 9}. 3. **Finding (A ∩ B) (the intersection of A and B)**: - The intersection A ∩ B consists of all elements that are in both A and B: - A ∩ B = {1, 2, 5} ∩ {3, 6, 7} = {} (There are no common elements). So the final results are: - A' = {3, 4, 6, 7, 8, 9} - B' = {1, 2, 4, 5, 8, 9} - (A ∩ B) = {}.