We are given the universal set $U = \{a, b, c, d, e, f, g, h, i, j\}$ and three sets:

• $A = \{a, b, e, g\}$
• $B = \{a, c, g, h\}$
• $C = \{b, g, h, j\}$

We need to find the elements of the set $A \cap (B \cup C)$.

Step 1: Find $B \cup C$ (the union of sets B and C)

The union of two sets includes all the elements that are in either one or both of the sets. Therefore: $B \cup C = \{a, b, c, g, h, j\}$

Step 2: Find $A \cap (B \cup C)$ (the intersection of A with $B \cup C$)

The intersection of two sets includes only the elements that are present in both sets. So, we now find the elements that are in both $A = \{a, b, e, g\}$ and $B \cup C = \{a, b, c, g, h, j\}$.

The common elements between $A$ and $B \cup C$ are: $A \cap (B \cup C) = \{a, b, g\}$

Thus, the set $A \cap (B \cup C)$ is $\{a, b, g\}$.

Would you like further details or have any questions?

Here are some related questions:

1. What is the intersection $A \cap B$?
2. What is the union $A \cup C$?
3. What is the complement of set $A$ in the universal set $U$?
4. What is the result of $(A \cup B) \cap C$?
5. How would you find $A \cap B \cap C$?

Tip: The intersection of two sets always contains elements common to both, whereas the union contains all elements from both sets.