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The task is to find the union of the sets \( T \) and \( W \).

Given:

\[
T = \{1, 3, 6, 7\}
\]
\[
W = \{3, 4, 7, 9\}
\]

The union of two sets, denoted \( T \cup W \), includes all the distinct elements that are in either set \( T \), set \( W \), or both.

### Steps:
1. Combine all elements from sets \( T \) and \( W \).
2. Remove any duplicates to ensure all elements in the union are distinct.

From set \( T \):
\[
\{1, 3, 6, 7\}
\]
From set \( W \):
\[
\{3, 4, 7, 9\}
\]

Combining the elements:
\[
\{1, 3, 6, 7, 3, 4, 7, 9\}
\]

Removing duplicates:
\[
\{1, 3, 4, 6, 7, 9\}
\]

### Therefore, the union of sets \( T \) and \( W \) is:
\[
T \cup W = \{1, 3, 4, 6, 7, 9\}
\]

Would you like further details or explanations? Here are five related questions to consider:

1. What is the intersection of \( T \) and \( W \)?
2. What does the complement of set \( T \) look like if the universal set is the integers from 1 to 10?
3. How would you find the difference \( T - W \)?
4. If we define a new set \( U = \{2, 5, 8\} \), what is \( T \cup W \cup U \)?
5. What are the properties of set operations (e.g., commutativity of union)?

**Tip:** In set theory, the union operation combines all elements, but duplicates are counted only once.

Write down all of the numbers that are in the union of sets T = {1, 3, 6, 7} and W = {3, 4, 7, 9}.

Learn how to find the union of two sets: T = {1, 3, 6, 7} and W = {3, 4, 7, 9}. The union includes all distinct elements from both sets, ensuring no duplicates. Ideal for students in Grades 6-8.

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