Find the complement of the set given that 

*U* = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

 (Enter your answers as a comma-separated list.)

{*x* | *x*  *W* and *x* < 8}

The universal set \( U \) is given as:

\[
U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}
\]

The given set is:

\[
A = \{x \ | \ x \in W \ \text{and} \ x < 8\}
\]

Here, \( W \) represents the set of whole numbers, and whole numbers include all non-negative integers. Thus, we are looking for values of \( x \) from \( U \) that are less than 8. Therefore, the set \( A \) will include:

\[
A = \{0, 1, 2, 3, 4, 5, 6, 7\}
\]

The complement of a set \( A \), denoted \( A^c \), is the set of elements in \( U \) that are not in \( A \). So the complement of \( A \) is:

\[
A^c = U - A = \{8, 9, 10, 11, 12\}
\]

Thus, the complement of the set is:

\[
A^c = \{8, 9, 10, 11, 12\}
\]

Do you have any questions or need further clarification?

Here are some related questions for practice:
1. What is the complement of the set \( \{2, 4, 6\} \) in \( U = \{0, 1, 2, 3, 4, 5, 6, 7\} \)?
2. If \( A = \{1, 2, 3, 4\} \) and \( B = \{3, 4, 5, 6\} \), what is \( A^c \cap B \)?
3. Find the union of sets \( A = \{0, 2, 4\} \) and \( B = \{1, 2, 3\} \).
4. What is the intersection of \( A = \{1, 3, 5, 7\} \) and \( B = \{2, 3, 6\} \)?
5. If \( U = \{a, b, c, d, e\} \), what is the complement of \( A = \{b, d\} \)?

**Tip:** The complement of a set always contains every element from the universal set that is not in the original set.

Find the complement of the set given that U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. (Enter your answers as a comma-separated list.) {x | x W and x < 8}

Find the complement of a set given the universal set U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}. This problem involves understanding the concept of set complement in set theory, suitable for students in Grades 6-8.

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