The union of two sets, denoted $A \cup U$, consists of all distinct elements that are in either set $A$ or set $U$ (or in both). To find $A \cup U$, we combine all elements from both sets and remove any duplicates.

Given:

• $U = \{1, 2, 3, 4, 5, 6, 7, 8\}$
• $A = \{2, 4, 5, 8\}$

The union $A \cup U$ is:

$A \cup U = \{1, 2, 3, 4, 5, 6, 7, 8\}$

This is because all elements of $A$ are already in $U$, so the union is just the set $U$.

Answer: $A \cup U = \{1, 2, 3, 4, 5, 6, 7, 8\}$

Would you like any further details or clarification?

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Related Questions:

1. What is the intersection of sets $A$ and $U$?
2. How do you find the complement of set $A$ with respect to $U$?
3. What is the difference $U - A$ (the elements in $U$ but not in $A$)?
4. What is the power set of $U$?
5. How do you perform a symmetric difference of sets $A$ and $U$?

Tip: When performing set operations like union and intersection, remember that the union includes all elements from both sets without repetition, while the intersection includes only the elements that appear in both sets.