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Use [tex]U=\{1,2,3,4,5,6,7,8,9,10\}[/tex], [tex]A=\{2,4,5\}[/tex], [tex]B=\{5,6,7,8\}[/tex], and [tex]C=\{2,5,7\}[/tex] to find the given set.

[tex]\bar{A}[/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. [tex]\bar{A}=[/tex] [tex]$\square$[/tex]
(Use a comma to separate answers as needed.)

B. The solution is the empty set.

Sagot :

GinnyAnsweridn
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]
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