The set $S = \{1, 2, 3, 4, 5, 6, 7\}$ is partitioned into three pairwise disjoint subsets $A$, $B$, and $C$ such that $1 \in A$, $2 \in B$, and $3 \in C$. If $A \cup B = \{1, 2, 4, 5, 6\}$, $B \cup C = \{2, 3, 5, 6, 7\}$, and $n(B) = 3$, find the set $B$.