Let’s analyze the question from the uploaded image:

Problem:

We are asked to find $(C \cup B) \cap A'$ using the given Venn diagram. The notation and symbols mean the following:

• $C \cup B$: The union of sets $C$ and $B$, which includes all elements belonging to either $C$ or $B$.
• $A'$: The complement of set $A$, which includes all elements not in $A$.
• $(C \cup B) \cap A'$: The intersection of $C \cup B$ and $A'$, i.e., the elements that are in both $C \cup B$ and $A'$.

Step-by-Step Solution:

1. Identify $C \cup B$: From the Venn diagram, $C \cup B$ includes all elements in either set $C$ or $B$. These elements are:

   • $p, q, s, t, x, y, g, h$.

2. Identify $A'$: The complement of $A$, $A'$, includes all elements not in $A$. From the diagram, $A'$ contains:

   • $p, q, g, h$.

3. Find the intersection $(C \cup B) \cap A'$: Now, we find the common elements between $C \cup B$ and $A'$. The elements shared between $\{p, q, s, t, x, y, g, h\}$ (from $C \cup B$) and $\{p, q, g, h\}$ (from $A'$) are:

   • $p, q, g, h$.

Final Answer:

The result of $(C \cup B) \cap A'$ is: $\{ p, q, g, h \}$

Would you like me to go into further detail about any of the steps?

5 Related Questions:

1. How do you find the union ($\cup$) and intersection ($\cap$) of two sets in general?
2. What is the significance of the complement of a set ($A'$) in set theory?
3. Can you explain how Venn diagrams help in visualizing set operations?
4. How do you find the elements of $(A \cup C) \cap B$ using the same Venn diagram?
5. What happens if all sets $A, B,$ and $C$ overlap entirely? How would this change the operations?

Tip:

When working with Venn diagrams, label all sets carefully and shade regions corresponding to unions, intersections, and complements. This helps in avoiding errors during calculations!