Let U = 
{5, 6, 7, 8, 9, 10, 11, 12},
  A = 
{6, 8, 10},
  B = 
{5, 6, 9, 12},
 and C = 
{5, 7, 9}
. Find the following. (Enter your answers as a comma-separated list.)
(A ∪ B)'

We are tasked with finding the complement of \( A \cup B \), denoted as \( (A \cup B)' \), where \( U \) is the universal set.

### Step-by-Step Solution:

1. **Union of sets \( A \) and \( B \):**
   - The union \( A \cup B \) consists of all elements that are in either \( A \) or \( B \), or in both.
   - \( A = \{6, 8, 10\} \)
   - \( B = \{5, 6, 9, 12\} \)

   Therefore:
   \[
   A \cup B = \{5, 6, 8, 9, 10, 12\}
   \]

2. **Complement of \( A \cup B \):**
   - The complement of \( A \cup B \) consists of all elements in the universal set \( U \) that are **not** in \( A \cup B \).
   - Universal set \( U = \{5, 6, 7, 8, 9, 10, 11, 12\} \)
   - \( A \cup B = \{5, 6, 8, 9, 10, 12\} \)

   The elements in \( U \) that are not in \( A \cup B \) are:
   \[
   (A \cup B)' = \{7, 11\}
   \]

### Final Answer:
\[
(A \cup B)' = 7, 11
\]

Would you like more details, or do you have any questions? Here are some related questions you can explore:

1. What is \( (A \cap B)' \) for the same sets?
2. How do you find \( (A \cup C)' \)?
3. What is the union of \( B \cup C \)?
4. How do you compute \( A' \cup B' \)?
5. What is \( (A \cup B \cup C)' \)?

**Tip:** When taking the complement of a set, always compare it with the universal set.

Let U = {5, 6, 7, 8, 9, 10, 11, 12}, A = {6, 8, 10}, B = {5, 6, 9, 12}, and C = {5, 7, 9}. Find the following. (Enter your answers as a comma-separated list.) (A ∪ B)'

Learn how to compute the complement of the union of two sets A and B, with detailed step-by-step solutions. Explore key set theory concepts like union and complement, using the universal set U = {5, 6, 7, 8, 9, 10, 11, 12}. Suitable for students in Grades 8-10.

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