To find the union of two sets, denoted [tex]\( A \cup B \)[/tex], we compile all the unique elements that are in either set [tex]\( A \)[/tex] or set [tex]\( B \)[/tex].
Given the sets:
[tex]\[ A = \{7, 8, 10, 11, 15, 16, 17, 18, 19\} \][/tex]
[tex]\[ B = \{1, 2, 3, 5, 15, 16, 20\} \][/tex]
We need to list all the unique elements from both sets:
1. Start by listing all the elements of set [tex]\( A \)[/tex]:
[tex]\[ 7, 8, 10, 11, 15, 16, 17, 18, 19 \][/tex]
2. Now list all the elements of set [tex]\( B \)[/tex]:
[tex]\[ 1, 2, 3, 5, 15, 16, 20 \][/tex]
3. Combine these two lists:
[tex]\[ 7, 8, 10, 11, 15, 16, 17, 18, 19, 1, 2, 3, 5, 15, 16, 20 \][/tex]
4. Remove the duplicates (elements that appear in both sets):
[tex]\[ 1, 2, 3, 5, 7, 8, 10, 11, 15, 16, 17, 18, 19, 20 \][/tex]
The unique elements in [tex]\( A \cup B \)[/tex] are:
[tex]\[ A \cup B = \{1, 2, 3, 5, 7, 8, 10, 11, 15, 16, 17, 18, 19, 20\} \][/tex]
So the final answer is:
[tex]\[ A \cup B = \{1, 2, 3, 5, 7, 8, 10, 11, 15, 16, 17, 18, 19, 20\} \][/tex]
