Final answer:
Using De Morgan's Law with sets U, A, and B, we calculated the intersection of A and B and its complement, as well as the complements of A and B individually and their union, to verify that (A ∩ B)' = A' ∪ B'.
Step-by-step explanation:
De Morgan's Law states that for any two sets A and B, the complement of the intersection of A and B is equal to the union of the complements of A and B. Symbolically, this can be expressed as (A ∩ B)' = A' ∪ B'. To prove this using the given sets U = {3, 4, 7, 9, 11, 18, 19, 20}, A = {7, 9, 11, 20}, and B = {7, 11, 18}, we first find the intersection of A and B, which is A ∩ B = {7, 11}. The complement of this intersection inside the universe U is (A ∩ B)' = {3, 4, 9, 18, 19, 20}. Next, we determine the complements of A and B individually within U: A' = {3, 4, 18, 19}, and B' = {3, 4, 9, 19, 20}. Finally, the union of A' and B' is A' ∪ B' = {3, 4, 9, 18, 19, 20}, which is exactly equal to (A ∩ B)', thus confirming De Morgan's Law.