Sure, let's find the union of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex]. The union of two sets includes all the elements that are present in either of the sets.
Given:
[tex]\[ A = \{1, 2, 3, 4, 6, 8, 10\} \][/tex]
[tex]\[ B = \{1, 3, 5, 7, 8, 9\} \][/tex]
To find [tex]\( A \cup B \)[/tex], we combine all the unique elements from both sets. We list each element from [tex]\( A \)[/tex] and then add those elements from [tex]\( B \)[/tex] that are not already in [tex]\( A \)[/tex].
1. Start with all elements in [tex]\( A \)[/tex]:
[tex]\[ \{1, 2, 3, 4, 6, 8, 10\} \][/tex]
2. Add elements from [tex]\( B \)[/tex] that are not in [tex]\( A \)[/tex]:
[tex]\[ \{1, 2, 3, 4, 6, 8, 10\} \cup \{5, 7, 9\} = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \][/tex]
Thus, the union [tex]\( A \cup B \)[/tex] is:
[tex]\[ \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \][/tex]
