To find the complement of set A with respect to the universal set U, we can follow these steps:
### Step-by-Step Solution:
1. **Identify the Universal Set and Set A**:
- The universal set \( U = \{1, 2, 3, 4, 5, 6, 7, 8\} \)
- The set \( A = \{1, 2, 3, 4\} \)
2. **Determine the Elements of Set A**:
- The elements in set A are 1, 2, 3, and 4.
3. **Find the Complement of Set A**:
- The complement of set A, denoted as \( A^C \) or \( A' \), consists of all the elements in the universal set U that are not in set A.
- To find \( A^C \), we subtract the elements of set A from the universal set U.
4. **Perform the Subtraction**:
- From the universal set \( U \), remove the elements of set \( A \):
\[
A^C = U - A = \{1, 2, 3, 4, 5, 6, 7, 8\} - \{1, 2, 3, 4\}
\]
5. **List the Remaining Elements**:
- After removing 1, 2, 3, and 4 from U, we are left with:
\[
A^C = \{5, 6, 7, 8\}
\]
### Final Answer:
Thus, the complement of set A, \( A^C \), is equal to \( \{5, 6, 7, 8\} \).
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