To find the set [tex]\( A \cup B \)[/tex] (the union of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex]), we combine all the unique elements present in either set [tex]\( A \)[/tex] or set [tex]\( B \)[/tex].
Given:
[tex]\[ U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \][/tex]
[tex]\[ A = \{1, 2, 4, 7\} \][/tex]
[tex]\[ B = \{3, 1, 5\} \][/tex]
We need to combine all the elements from sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] without repeating any elements.
Listing out the elements in [tex]\( A \)[/tex]:
[tex]\[ A = \{1, 2, 4, 7\} \][/tex]
Listing out the elements in [tex]\( B \)[/tex]:
[tex]\[ B = \{3, 1, 5\} \][/tex]
Now, we combine both sets, making sure to include each element only once:
[tex]\[ A \cup B = \{1, 2, 3, 4, 5, 7\} \][/tex]
Thus, we find that [tex]\( A \cup B = \{1, 2, 3, 4, 5, 7\} \)[/tex].
So the correct choice is:
A. [tex]\( A \cup B = \{1, 2, 3, 4, 5, 7\} \)[/tex]
