To solve this, let's break it down step-by-step using the sets provided:

1. Identify the union of sets B and C:

   • Set B = {5, 6, 7, 8}
   • Set C = {2, 4, 6, 8, 9}

   The union of two sets $B \cup C$ includes all the elements from both sets, without duplicates: $B \cup C = \{2, 4, 5, 6, 7, 8, 9\}$

2. Now, find the intersection of set A with $B \cup C$:

   • Set A = {3, 4, 5, 6}
   • $B \cup C = \{2, 4, 5, 6, 7, 8, 9\}$

   The intersection of two sets $A \cap (B \cup C)$ includes only the elements that are present in both sets A and $B \cup C$: $A \cap (B \cup C) = \{4, 5, 6\}$

Thus, the elements of $A \cap (B \cup C)$ are {4, 5, 6}.

Final answer choices:

The correct answer is {4, 5, 6}.

Would you like more details or have any questions?

Related questions:

1. What is the difference between the union and intersection of sets?
2. How can you perform the union of two sets in a different way using set operations?
3. What happens when you take the intersection of three sets?
4. How do you find the union of more than two sets?
5. What are the properties of intersection and union in set theory?

Tip:

When performing union and intersection operations, it's helpful to write down all elements explicitly to avoid missing anything.