Let's verify each of these statements using set operations:
(i) To verify (A ∪ B)' = A' ∩ B':
1. First, let's find A ∪ B:
A ∪ B = {-3, -2, -1, 0, 1, 3, 4}
2. Now, find the complement of A ∪ B, denoted as (A ∪ B)':
(A ∪ B)' = {-4, -2, 2}
3. Next, let's find the complements of sets A and B:
A' = {-4, -2, 0, 2, 4}
B' = {-1, 1, 2}
4. Now, find the intersection of A' and B':
A' ∩ B' = {-2, 2}
Comparing the results, we see that (A ∪ B)' = A' ∩ B', so the statement (i) is verified.
(ii) To verify (AB)' = A' ∪ B':
1. First, let's find the intersection of A and B:
A ∩ B = {-3, 3}
2. Now, find the complement of A ∩ B, denoted as (A ∩ B)':
(A ∩ B)' = {-4, -3, -2, -1, 0, 1, 2, 4}
3. Next, let's find the complements of sets A and B:
A' = {-4, -2, 0, 2, 4}
B' = {-1, 1, 2}
4. Now, find the union of A' and B':
A' ∪ B' = {-4, -2, -1, 0, 1, 2, 4}
Comparing the results, we see that (AB)' = A' ∪ B', so the statement (ii) is verified.
Therefore, both statements hold true.
