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Part 1
Let Uequals​{a, ​b, c,​ d, e,​ f, g,​ h, i,​ j, k},
    Aequals​{a​, b​, d​, f​, h​, k​},
    Bequals​{b​, d​, f​, h​, j​},
    Cequals​{a​, b​, g​, j​, k​}.
Determine Upper A union left parenthesis Upper C intersect Upper B right parenthesis prime.


To find \( A \cup (C \cap B)' \), let's follow the steps:

1. **Find \( C \cap B \)**:
   - \( C = \{ a, b, g, j, k \} \)
   - \( B = \{ b, d, f, h, j \} \)
   - \( C \cap B = \{ b, j \} \)

2. **Find \( (C \cap B)' \)**:
   - The universal set \( U = \{ a, b, c, d, e, f, g, h, i, j, k \} \)
   - \( (C \cap B)' \) includes all elements in \( U \) that are not in \( C \cap B \):
   - \( (C \cap B)' = \{ a, c, d, e, f, g, h, i, k \} \)

3. **Find \( A \cup (C \cap B)' \)**:
   - \( A = \{ a, b, d, f, h, k \} \)
   - \( (C \cap B)' = \{ a, c, d, e, f, g, h, i, k \} \)
   - \( A \cup (C \cap B)' = \{ a, b, c, d, e, f, g, h, i, k \} \)

Thus, \( A \cup (C \cap B)' = \{ a, b, c, d, e, f, g, h, i, k \} \).

Would you like more details or have any questions about this solution? Here are some related questions:

1. What are the elements of \( A \cap B \)?
2. Can you explain how to find the complement of a set?
3. What is the significance of unions and intersections in set theory?
4. How would you represent these sets using Venn diagrams?
5. What would change if the universal set were different? 

**Tip**: Always double-check the elements when finding intersections or complements!

Let U={a, b, c, d, e, f, g, h, i, j, k}, A={a, b, d, f, h, k}, B={b, d, f, h, j}, C={a, b, g, j, k}. Determine A ∪ (C ∩ B)'.

Explore the solution to the problem of determining A ∪ (C ∩ B)' using set operations. This detailed breakdown covers key concepts in set theory, including unions, intersections, and complements, suitable for students in Grades 9-11.

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