To find the union of two sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex], denoted as [tex]\( A \cup B \)[/tex], we combine all the unique elements from both sets without repetition.
Given the sets:
[tex]\[ A = \{1, 2, 3, 4, 6, 8, 10\} \][/tex]
[tex]\[ B = \{1, 3, 5, 7, 8, 9\} \][/tex]
We'll go through each element in both sets:
1. List all the elements from set [tex]\( A \)[/tex]: [tex]\( \{1, 2, 3, 4, 6, 8, 10\} \)[/tex]
2. Then, add the elements from set [tex]\( B \)[/tex] that are not already in set [tex]\( A \)[/tex]:
- 1 (already in [tex]\( A \)[/tex])
- 3 (already in [tex]\( A \)[/tex])
- 5 (not in [tex]\( A \)[/tex], add it)
- 7 (not in [tex]\( A \)[/tex], add it)
- 8 (already in [tex]\( A \)[/tex])
- 9 (not in [tex]\( A \)[/tex], add it)
Combining these, the union of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is:
[tex]\[ A \cup B = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \][/tex]
Therefore, the union [tex]\( A \cup B \)[/tex] is:
[tex]\[ \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \][/tex]
