Given the following sets, find the set $(A \cup B \cup C)^{\prime}$.
\[
\begin{array}{l}
U=\{1,2,3, \ldots, 7\} \\
A=\{1,3,6,7\} \\
B=\{2,6,7\} \\
C=\{2,3,4,5,7\}
\end{array}
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $(A \cup B \cup C)^{\prime}=$
(Use a comma to separate answers as needed. Use ascending order.)
B. $(A \cup B \cup C)^{\prime}$ is the empty set.

Step 1 ：Given the universal set U = \{1, 2, 3, 4, 5, 6, 7\}, and the sets A = \{1, 3, 6, 7\}, B = \{2, 6, 7\}, and C = \{2, 3, 4, 5, 7\}.

Step 2 ：The question is asking for the complement of the union of sets A, B, and C. The union of sets A, B, and C would include all elements that are in any of these sets. The complement of this union would then be all elements in the universal set U that are not in the union of A, B, and C.

Step 3 ：To solve this, we first find the union of sets A, B, and C. The union of A, B, and C is \{1, 2, 3, 4, 5, 6, 7\}.

Step 4 ：Then, we find the complement of this union by finding all elements in U that are not in the union of A, B, and C. The complement of the union of sets A, B, and C is an empty set.

Step 5 ：This means that all elements in the universal set U are included in the union of sets A, B, and C. Therefore, there are no elements in U that are not in the union of A, B, and C.

Step 6 ：Final Answer: \(\boxed{(A \cup B \cup C)^{\prime}\text{ is the empty set}}\)