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

Let A = {a, b, e, g}, B = {a, c, g, h}, and C = {b, g, h, j}

List the elements of the set A∩(B∪C)A∩(B∪C)

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.

Let the Universal set be the letters a through j: U = {a, b, ..., i, j}. Let A = {a, b, e, g}, B = {a, c, g, h}, and C = {b, g, h, j}. List the elements of the set A∩(B∪C).

Learn how to solve the set theory problem involving the intersection of set A with the union of sets B and C. This example uses the universal set U = {a, b, c, d, e, f, g, h, i, j}, with step-by-step instructions for finding A∩(B∪C). Suitable for Grades 8-10 students.

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