(3) Let there be a non-empty set $A \subseteq\{1,2,3,4,5,6,7\}$, and when $a \in A$, it must also be that $8-a \in A$. The number of such sets $A$ is $\qquad$.
(3) 15 Hint: First find the sets of units and binary sets that meet the requirements: $A_{1}=\{4\}, A_{2}=\{1,7\}, A_{3}=$ $\{2,6\}, A_{4}=\{3,5\}$. The problem is equivalent to finding the number of non-empty subsets of $\left\{A_{1}, A_{2}, A_{3}, A_{4}\right\}$, hence: $2^{4}-1=15$ (sets).