If A = [1,2,5,7] and B = [1,3,5,7] are subset of the universe U [1,2,3...10], Find A'uB
To find A'uB, we first need to find the complement of A (Au) and the complement of B (Bu), and then find the union of these two complements.
Complement of A (Au):
Since A is a subset of U, the complement of A would be the elements in U that are not in A.
Complement of A = [3,4,6,8,9,10]
Complement of B (Bu):
Since B is a subset of U, the complement of B would be the elements in U that are not in B.
Complement of B = [2,4,6,8,9,10]
Now, we find the union of Au and Bu:
A'uB = [3,4,6,8,9,10] U [2,4,6,8,9,10]
= [2,3,4,6,8,9,10]
Therefore, A'uB = [2,3,4,6,8,9,10]
To find the complement of a set A, denoted as A', we need to identify all the elements in the universe U that are not in set A.
Given: A = [1, 2, 5, 7] and B = [1, 3, 5, 7] are subsets of the universe U = [1, 2, 3, ..., 10].
First, let's find the complement of set A (A'):
1. List all the elements in universe U: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10].
2. Remove all the elements that are in set A from universe U: [3, 4, 6, 8, 9, 10].
Now, let's find the union of set A' and set B (A' U B):
1. List all the elements in set A': [3, 4, 6, 8, 9, 10].
2. Add the elements from set B that are not already in set A': [3, 4, 6, 8, 9, 10, 3].
Note: The element '3' is included only once because it appears in both sets A' and B.
Therefore, the set A' U B is [3, 4, 6, 8, 9, 10].