Given the following​ sets, find the set Upper A union left parenthesis Upper B intersect Upper C right parenthesis.
Uequals​{​1, ​2, 3, . .​ ., 6​}
Aequals​{1​, 2​, 3​, 4​}
Bequals​{1​, 2​, 3​}
Cequals​{1​, 2​, 3​, 4​, 5​}

Let's break this down step by step:

### Step 1: Understand the sets.
We are given the following sets:
- \( U = \{1, 2, 3, \dots, 6\} \)
- \( A = \{1, 2, 3, 4\} \)
- \( B = \{1, 2, 3\} \)
- \( C = \{1, 2, 3, 4, 5\} \)

### Step 2: Find \( B \cap C \).
The intersection of sets \( B \) and \( C \) includes all the elements that are common to both sets:
- \( B = \{1, 2, 3\} \)
- \( C = \{1, 2, 3, 4, 5\} \)

So, \( B \cap C = \{1, 2, 3\} \).

### Step 3: Find \( A \cup (B \cap C) \).
Now we need to find the union of set \( A \) with \( B \cap C \):
- \( A = \{1, 2, 3, 4\} \)
- \( B \cap C = \{1, 2, 3\} \)

The union of these two sets includes all the elements from both sets, without duplicates:
- \( A \cup (B \cap C) = \{1, 2, 3, 4\} \)

### Final Answer:
\[ A \cup (B \cap C) = \{1, 2, 3, 4\} \]

Would you like further details or have any questions?

Here are 5 related questions:
1. How is the intersection of two sets different from their union?
2. What would be the result of \( B \cup C \)?
3. Can you calculate \( A \cap B \)?
4. How would the union change if \( A \) had more elements than \( B \cap C \)?
5. What is the difference between complement and intersection in set theory?

**Tip:** The union of two sets contains all unique elements from both sets, while the intersection contains only elements common to both sets.

Given the following sets, find the set A union (B intersect C). U = {1, 2, 3, ..., 6}, A = {1, 2, 3, 4}, B = {1, 2, 3}, C = {1, 2, 3, 4, 5}.

Discover how to find the union of set A and the intersection of sets B and C. This step-by-step guide explains the concepts of union and intersection in set theory, using specific sets U = {1, 2, 3, ..., 6}, A = {1, 2, 3, 4}, B = {1, 2, 3}, and C = {1, 2, 3, 4, 5}. Suitable for Grades 6-8.

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