give the following determine the set
(A'U'B)n(AUB)'
U ={1,2,3,4,5,6,7,8}
A={1,2,3,7,8}
B={1,3,4,6}
To determine the set (A' ∪ B) ∩ (A ∪ B)', we first need to find the complement of each set.
1. Find A':
The complement of set A, denoted as A', consists of all the elements in the universal set U that are not in A. From the given information, we have:
U = {1,2,3,4,5,6,7,8}
A = {1,2,3,7,8}
A' = U - A = {4,5,6}
2. Find B':
Similarly, the complement of set B, denoted as B', consists of all the elements in the universal set U that are not in B. From the given information, we have:
U = {1,2,3,4,5,6,7,8}
B = {1,3,4,6}
B' = U - B = {2,5,7,8}
3. Evaluate (A ∪ B):
(A ∪ B) refers to the union of sets A and B. It consists of all the elements that are in A or B, including any duplicates. From the given information, we have:
A = {1,2,3,7,8}
B = {1,3,4,6}
(A ∪ B) = {1,2,3,4,6,7,8}
4. Find (A ∪ B)':
The complement of the set (A ∪ B), denoted as (A ∪ B)', consists of all the elements in the universal set U that are not in (A ∪ B). From the given information, we have:
U = {1,2,3,4,5,6,7,8}
(A ∪ B) = {1,2,3,4,6,7,8}
(A ∪ B)' = U - (A ∪ B) = {5}
5. Evaluate (A' ∪ B) ∩ (A ∪ B)':
To determine the set (A' ∪ B) ∩ (A ∪ B)', we take the union of sets A' and B, then find the intersection with the complement of (A ∪ B).
(A' ∪ B) = {4,5,6} ∪ {1,3,4,6} = {1,3,4,5,6}
(A ∪ B)' = {5}
(A' ∪ B) ∩ (A ∪ B)' = {1,3,4,5,6} ∩ {5} = {5}
Therefore, (A' ∪ B) ∩ (A ∪ B)' is the set {5}.