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.