Final answer:
The set A' ∩ B' represents elements not in A and not in B. To list elements in A' ∩ B', identify items not in each set separately, then find their intersection. A' = B implies A' intersect B' = A'.
Step-by-step explanation:
To list all the elements of the set (A complement intersect B complement), denoted as A' ∩ B', we first need to determine the elements that are not in A (A') and the elements that are not in B (B').
The intersection of A' and B' will then give us the elements that are neither in A nor in B.
For example, if we have a universal sample space S = {1, 2, 3, 4, 5, 6} and let A = {1, 2, 3, 4}, then A' (the complement of A) would be {5, 6}. If B is such that A' = B, then we already have that A' ∩ B' = A'.
This is because A and B are complements in this scenario, and the intersection of two identical sets is the set itself.
If we were given specific sets for both A and B, we would identify the elements not in A and not in B separately, and then find the common elements between A' and B' for the final answer.
For example, if B = {3, 4, 5, 6} in the same sample space S, then B' would be {1, 2}, and subsequently A' ∩ B' = {5, 6} ∩ {1, 2} = ∅ (the empty set), as there are no common elements in A' and B'.