To find the set $A \cup B$, we need to determine the union of sets $A$ and $B$.

1. Identify the elements of sets $A$ and $B$:

   • $A = \{1, 4, 5\}$
   • $B = \{5, 7, 8, 9\}$

2. Find the union of $A$ and $B$:

   • The union $A \cup B$ includes all elements that are in $A$, $B$, or both.
   • Combine the elements from both sets without repeating any element.

   $A \cup B = \{1, 4, 5, 7, 8, 9\}$

So, the set $A \cup B$ is $\{1, 4, 5, 7, 8, 9\}$.

Would you like any details on this solution or have any further questions? Here are some related questions:

1. How do you find the intersection of two sets?
2. What is the complement of the union of two sets?
3. Can the union of two sets be smaller than one of the original sets?
4. How do you find the union of more than two sets?
5. What is the difference between union and intersection of sets?

Tip: The union of sets combines all unique elements from both sets. If an element is in both sets, it only appears once in the union.