Let the Universal set be the letters a through j: U = {a, b, ..., i, j}.

Let A = {a, b, c, g}, B = {b, f, g, h}, and C = {c, d, f, g}

List the elements of the set A∩(B∪C)

To find the elements of the set \(A \cap (B \cup C)\), we'll follow these steps:

### Step 1: Find \(B \cup C\)
The union of sets \(B\) and \(C\) (denoted \(B \cup C\)) includes all elements that are in either \(B\) or \(C\):

\[
B = \{b, f, g, h\}
\]
\[
C = \{c, d, f, g\}
\]

So,

\[
B \cup C = \{b, c, d, f, g, h\}
\]

### Step 2: Find \(A \cap (B \cup C)\)
Now, we find the intersection of set \(A\) with \(B \cup C\). The intersection (denoted \(A \cap (B \cup C)\)) includes all elements that are in both \(A\) and \(B \cup C\):

\[
A = \{a, b, c, g\}
\]
\[
B \cup C = \{b, c, d, f, g, h\}
\]

The common elements between \(A\) and \(B \cup C\) are \(b\), \(c\), and \(g\).

Thus,

\[
A \cap (B \cup C) = \{b, c, g\}
\]

So, the elements of the set \(A \cap (B \cup C)\) are:

\(\boxed{\{b, c, g\}}\)

Do you need any more details or have any questions?

---

1. How would you find \(A \cup (B \cap C)\)?
2. What is the complement of set \(A\) with respect to \(U\)?
3. Can you list the elements of \(A \cap B \cap C\)?
4. How do you determine the difference \(A - B\)?
5. What would be the result of \(A \cup (B \cup C)\)?

**Tip:** The union of sets combines all unique elements, while the intersection selects only the elements common to both sets.

Discover how to find the elements of the set A intersect (B union C) using set theory. This problem involves sets A, B, and C, and covers key concepts such as union and intersection of sets. Suitable for high school students studying set theory.

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