https://file.aiquickdraw.com/mathbot/file/1727326249317kt346pph.jpg

Let's break down the two parts of the problem to understand how the shading should be applied to the Venn diagrams:

### Part (a): \( Q' \cap R \)
- **\( Q' \)** represents the complement of set \( Q \), meaning all elements *outside* of \( Q \).
- **\( R \)** is just the set \( R \).
- The intersection \( Q' \cap R \) means we are interested in the region that is in \( R \) but *not* in \( Q \).

In the Venn diagram for part (a), you should:
- Shade the region where \( R \) is, but ensure that you do **not** shade the part that overlaps with \( Q \). Only the portion of \( R \) that is outside of \( Q \) should be shaded.

### Part (b): \( P \cup (Q \cap R) \)
- **\( Q \cap R \)** is the intersection of \( Q \) and \( R \), meaning the area common to both sets.
- **\( P \cup (Q \cap R) \)** means you want the union of set \( P \) and the intersection \( Q \cap R \). This includes all elements in \( P \), as well as the elements common to both \( Q \) and \( R \).

In the Venn diagram for part (b), you should:
- Shade the entire region of \( P \).
- Also, shade the region where \( Q \) and \( R \) overlap, as this corresponds to \( Q \cap R \).

Would you like a detailed explanation of Venn diagrams and set operations?

### Related Questions:
1. What does the union of two sets represent on a Venn diagram?
2. How do you find the complement of a set in a Venn diagram?
3. What is the intersection of two sets, and how is it represented?
4. Can you explain how to shade the union of multiple sets on a Venn diagram?
5. How does the concept of universal sets impact the shading in Venn diagrams?

### Tip:
When working with Venn diagrams, start by identifying each set and the operations needed (e.g., union, intersection, or complement) before shading specific areas. This makes it easier to visualize the relationships between the sets.

7. The Venn diagram in the answer space shows the set P, set Q, and set R. Given that the universal set ξ = P ∪ Q ∪ R, on the diagram below, shade the set Q' ∩ R and P ∪ (Q ∩ R).

Solve a Venn diagram problem involving set operations. Learn how to shade regions for Q' ∩ R and P ∪ (Q ∩ R). This problem helps in understanding the complement, intersection, and union of sets using Venn diagrams. Suitable for students in Grades 9-12.

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