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To solve this problem, we need to calculate \( Q \cup (P - R) \) given the following sets:

- \( P = \{1, 6, 8, 22, 42\} \)
- \( Q = \{52, a, b, c, d, e, f\} \)
- \( R = \{1, 18, 42, 16, c, g, d, h\} \)

### Step 1: Calculate \( P - R \)
The operation \( P - R \) represents the elements in \( P \) that are not in \( R \).

- Elements of \( P \): \( \{1, 6, 8, 22, 42\} \)
- Elements of \( R \): \( \{1, 18, 42, 16, c, g, d, h\} \)

Comparing each element in \( P \) with \( R \):
- \( 1 \) is in \( R \), so it is excluded.
- \( 6 \) is not in \( R \), so it is included.
- \( 8 \) is not in \( R \), so it is included.
- \( 22 \) is not in \( R \), so it is included.
- \( 42 \) is in \( R \), so it is excluded.

Thus, \( P - R = \{6, 8, 22\} \).

### Step 2: Calculate \( Q \cup (P - R) \)
Now, we find the union of \( Q \) and \( P - R \), denoted by \( Q \cup (P - R) \).

- Elements of \( Q \): \( \{52, a, b, c, d, e, f\} \)
- Elements of \( P - R \): \( \{6, 8, 22\} \)

Taking the union of these two sets gives:
\[
Q \cup (P - R) = \{52, a, b, c, d, e, f, 6, 8, 22\}
\]

### Final Answer:
\[
Q \cup (P - R) = \{52, a, b, c, d, e, f, 6, 8, 22\}
\]

Would you like further clarification on any step?

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Here are five related questions that may deepen your understanding:
1. How do we determine the elements in \( P - R \) when both sets contain different types of elements (numbers and letters)?
2. What is the meaning of the union operation in set theory?
3. How would the result change if \( Q \) or \( R \) were different?
4. What would happen if we calculated \( P \cap R \) instead of \( P - R \)?
5. Can we determine \( Q \cap R \) with the given sets, and what would it represent?

**Tip:** Always double-check which elements are being removed in set difference operations, as it can easily lead to mistakes in complex sets.

Given that Set P = {1, 6, 8, 22, 42}, Q = {52, a, b, c, d, e, f} and R = {1, 18, 42, 16, c, g, d, h}, determine Q ∪ (P - R).

This problem involves calculating the union and difference of sets given three sets: P = {1, 6, 8, 22, 42}, Q = {52, a, b, c, d, e, f}, and R = {1, 18, 42, 16, c, g, d, h}. Learn how to find Q ∪ (P - R) with a step-by-step breakdown suitable for students in Grades 9-12.

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