To solve this, let's break it down step by step:

You are asked to find the elements of the set $A \cap (B \cup C)$.

1. Start with the Union $B \cup C$:

   • Set $B = \{ c, d, f, j \}$
   • Set $C = \{ a, c, i, j \}$
   • The union of two sets includes all elements from both sets without repetition: $B \cup C = \{ a, c, d, f, i, j \}$

2. Next, find the Intersection $A \cap (B \cup C)$:

   • Set $A = \{ a, b, f, j \}$
   • We now look for the elements that are common to both $A$ and $B \cup C$: $A \cap (B \cup C) = \{ a, f, j \}$

Thus, the elements of $A \cap (B \cup C)$ are $\{ a, f, j \}$.

Let me know if you'd like any further clarification or details!

Here are some related questions to explore:

1. What does the intersection of two sets represent?
2. How does the union of two sets differ from the intersection?
3. How would you find the union or intersection of more than two sets?
4. What would the set $A \cup (B \cap C)$ look like?
5. How can the universal set be useful when working with set operations?

Tip: Always remember that the union combines all elements, while the intersection only includes common elements!