Question 14Suppose that $S$ is a subset of $\left\{ 1, 2, 3, \cdots , 25 \right\}$ such that the sum of any two (not necessarily distinct) elements of $S$ is never an element of $S.$ What is the maximum number of elements $S$ may contain?$ \ 12 $$ \ 13 $$ \ 14 $$ \ 15 $$ \ 16 $