To find the complement of set [tex]\( A \)[/tex], denoted [tex]\(\bar{A}\)[/tex], we need to determine which elements are in the universal set [tex]\( U \)[/tex] but not in set [tex]\( A \)[/tex].
Given:
- Universal set [tex]\( U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \)[/tex]
- Set [tex]\( A = \{2, 4, 5\} \)[/tex]
The complement of [tex]\( A \)[/tex], [tex]\(\bar{A}\)[/tex], includes all the elements in [tex]\( U \)[/tex] that are not in [tex]\( A \)[/tex].
So, we remove the elements of [tex]\( A \)[/tex] from [tex]\( U \)[/tex]:
- Start with the universal set [tex]\( U \)[/tex]: \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}
- Remove 2 (in [tex]\( A \)[/tex]): \{1, 3, 4, 5, 6, 7, 8, 9, 10\}
- Remove 4 (in [tex]\( A \)[/tex]): \{1, 3, 5, 6, 7, 8, 9, 10\}
- Remove 5 (in [tex]\( A \)[/tex]): \{1, 3, 6, 7, 8, 9, 10\}
Thus, the elements that remain are \{1, 3, 6, 7, 8, 9, 10\}.
Therefore, the complement of [tex]\( A \)[/tex] is:
[tex]\[ \bar{A} = \{1, 3, 6, 7, 8, 9, 10\} \][/tex]
Therefore, the correct answer is:
A. [tex]\( \bar{A} = \{1, 3, 6, 7, 8, 9, 10\} \)[/tex]
