Given the following sets, find the set $A \cup(B \cap C)$.
\[
\begin{array}{l}
U=\{1,2,3, \ldots, 9\} \\
A=\{1,2,3,4\} \\
B=\{7,8,9\} \\
C=\{1,2,4,5,6\}
\end{array}
\]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $A \cup(B \cap C)=\{\}$
(Use a comma to separate answers as needed. Use ascending order.)
B. $A \cup(B \cap C)$ is the empty set.

Step 1 ：Given the sets A = {1, 2, 3, 4}, B = {7, 8, 9}, and C = {1, 2, 4, 5, 6}.

Step 2 ：First, we need to find the intersection of sets B and C, denoted as \(B \cap C\). The intersection of two sets is a set containing all elements that are common to both sets.

Step 3 ：Sets B and C have no common elements, so the intersection of sets B and C is an empty set.

Step 4 ：Next, we find the union of set A and the result of \(B \cap C\), denoted as \(A \cup(B \cap C)\). The union of two sets is a set containing all elements that are in either set.

Step 5 ：The union of set A and an empty set is set A itself.

Step 6 ：Therefore, the set \(A \cup(B \cap C)\) is equal to set A.

Step 7 ：Final Answer: \(A \cup(B \cap C)=\boxed{\{1,2,3,4\}}\)