The task is to compute the result of the operation $A \cup B \setminus C$, considering that the elements are part of the universal set $U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$.

Given Sets:

• $U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$
• $A = \{2, 4, 6, 8\}$
• $B = \{2, 3, 4, 5\}$
• $C = \{1, 3, 5, 7, 9\}$

Steps to Solve:

1. Union of $A \cup B$: Combine all unique elements of $A$ and $B$: $A \cup B = \{2, 4, 6, 8\} \cup \{2, 3, 4, 5\} = \{2, 3, 4, 5, 6, 8\}.$

2. Subtraction ($A \cup B \setminus C$): Remove all elements of $C$ from $A \cup B$: $A \cup B \setminus C = \{2, 3, 4, 5, 6, 8\} \setminus \{1, 3, 5, 7, 9\} = \{2, 4, 6, 8\}.$

3. Restrict to $U$: The result must only include elements from $U$, but since $\{2, 4, 6, 8\} \subseteq U$, this step does not affect the answer.

Final Answer:

The result of $A \cup B \setminus C$ is: $\{2, 4, 6, 8\}$

When formatted as the question specifies (numbers in ascending order, without spaces or commas), the answer is: $2468$

Would you like a detailed explanation of any step?

Related Questions:

1. What is the intersection of $A \cap B$?
2. How is the subtraction operation in sets defined mathematically?
3. What is the difference between $A \setminus B$ and $B \setminus A$?
4. How do we handle operations if $U$ is not a universal set?
5. How would the result change if $C = \emptyset$?

Tip:

To efficiently compute set operations, first write down each step and simplify before applying constraints like the universal set.