If the number of elements of a set whose all elements are positive integers is one more than the value of the smallest element of this set, this set is called a wide set. Let $A$, $B$, and $C$ be wide sets,
$A \cup B \cup C = \{ 1,2,3,4,5,6,7,8,9 \}$
$A \cap B = \{ 3 \}$
$1 \in A$
$6 \in B$
it is known that. Accordingly, which of the following is set $C$? A) $\{ 1,2 \}$ B) $\{ 3,4,8,9 \}$ C) $\{ 3,5,7,8 \}$ D) $\{ 4,5,6,7,8 \}$ E) $\{ 4,5,7,8,9 \}$
If the number of elements of a set whose all elements are positive integers is one more than the value of the smallest element of this set, this set is called a wide set.
Let $A$, $B$, and $C$ be wide sets,
\begin{itemize}
\item $A \cup B \cup C = \{ 1,2,3,4,5,6,7,8,9 \}$
\item $A \cap B = \{ 3 \}$
\item $1 \in A$
\item $6 \in B$
\end{itemize}
it is known that. Accordingly, which of the following is set $C$?\\
A) $\{ 1,2 \}$\\
B) $\{ 3,4,8,9 \}$\\
C) $\{ 3,5,7,8 \}$\\
D) $\{ 4,5,6,7,8 \}$\\
E) $\{ 4,5,7,8,9 \}$