Lindsey Murray
10/19/2023 · Senior High School
If \( A=\{x \mid x \) is an even integer \( \}, B=\{x \mid x \) is an odd integer\}, \( C=\{2,3,4,5\} \), and \( D=\{6,7,8,9\} \), list the element( \( s \) of the following set.
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To list the elements of the sets \( A \), \( B \), \( C \), and \( D \):
1. **Set \( A \)**: This set contains all even integers. The elements of \( A \) can be represented as:
\[
A = \{ \ldots, -4, -2, 0, 2, 4, 6, 8, \ldots \}
\]
Since this set is infinite, we cannot list all elements, but we can say it includes all integers of the form \( 2n \) where \( n \) is any integer.
2. **Set \( B \)**: This set contains all odd integers. The elements of \( B \) can be represented as:
\[
B = \{ \ldots, -5, -3, -1, 1, 3, 5, 7, 9, \ldots \}
\]
Similar to set \( A \), this set is also infinite and includes all integers of the form \( 2n + 1 \) where \( n \) is any integer.
3. **Set \( C \)**: This set contains the specific integers 2, 3, 4, and 5. Thus, we can list the elements as:
\[
C = \{2, 3, 4, 5\}
\]
4. **Set \( D \)**: This set contains the specific integers 6, 7, 8, and 9. Thus, we can list the elements as:
\[
D = \{6, 7, 8, 9\}
\]
If you need to perform operations or find specific combinations of these sets, please specify, and I can assist further!
Quick Answer
Set \( A \) includes all even integers, set \( B \) includes all odd integers, set \( C \) includes 2, 3, 4, 5, and set \( D \) includes 6, 7, 8, 9.
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