Let
U
​=
StartSet 3 comma 7 comma 8 comma 12 comma 11 comma 17 comma 20 comma 22 EndSet
A
​=
StartSet 3 comma 20 comma 22 EndSet
C
​=
StartSet 7 comma 8 comma 12 comma 11 comma 17 EndSet
Find Upper A union Upper C prime.
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Part 1
Choose the correct answer​ below, and, if​ necessary, fill in the answer box to complete your choice.


We are given the following sets:

- \( U = \{ 3, 7, 8, 12, 11, 17, 20, 22 \} \) (the universal set),
- \( A = \{ 3, 20, 22 \} \),
- \( C = \{ 7, 8, 12, 11, 17 \} \).

The task is to find \( A \cup C' \), where \( C' \) denotes the complement of set \( C \) relative to the universal set \( U \).

### Steps to Solve:

1. **Find \( C' \) (the complement of \( C \)):**
   The complement of set \( C \) consists of all the elements in \( U \) that are **not** in \( C \). So,
   \[
   C' = U - C = \{ 3, 7, 8, 12, 11, 17, 20, 22 \} - \{ 7, 8, 12, 11, 17 \} = \{ 3, 20, 22 \}.
   \]

2. **Find \( A \cup C' \) (the union of \( A \) and \( C' \)):**
   The union of two sets contains all the elements from both sets without repetition. We have:
   \[
   A = \{ 3, 20, 22 \}, \quad C' = \{ 3, 20, 22 \}.
   \]
   Therefore, the union is:
   \[
   A \cup C' = \{ 3, 20, 22 \} \cup \{ 3, 20, 22 \} = \{ 3, 20, 22 \}.
   \]

### Final Answer:
\[
A \cup C' = \{ 3, 20, 22 \}.
\]

If you need further clarification or additional examples, feel free to ask!

### Additional Questions:
1. What does the complement of a set mean in set theory?
2. How do you calculate the complement of a set relative to another set?
3. What is the difference between union and intersection in set theory?
4. How would the answer change if the universal set \( U \) were different?
5. Can you give an example where the union of two sets is empty?

### Tip:
When working with set operations, always carefully define the universal set, as the complement depends on it!

Let U = {3, 7, 8, 12, 11, 17, 20, 22}, A = {3, 20, 22}, C = {7, 8, 12, 11, 17}. Find A ∪ C' (complement of C).

Learn how to solve the problem of finding the union of set A and the complement of set C relative to the universal set U. This problem demonstrates key concepts in set theory such as the complement and union operations. Suitable for students in Grades 8-10.

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