17. Let $S$ be a set of positive integers, for example $S$ could consist of 3,4 , and 8 .
A positive integer $n$ is called an $S$-number if and only if for every factor $m$ of $n$ with $m > 1$, the number $m$ is a multiple of some number in $S$.
So in the above example, 9 is an $S$-number; this is because the factors of 9 greater than 1 are 3 and 9, and each of these is a multiple of 3 .
Positive integer $n$ is therefore not an $S$-number if and only if
A for every (positive) factor $m$ of $n$ with $m > 1$, there is a number in $S$ which is not a factor of $m$.
B for every (positive) factor $m$ of $n$ with $m > 1$, there is no number in $S$ which is a factor of $m$.
C for every (positive) factor $m$ of $n$ with $m > 1$, every number in $S$ is a factor of $m$.
D for some (positive) factor $m$ of $n$ with $m > 1$, there is a number in $S$ which is not a factor of $m$.
E for some (positive) factor $m$ of $n$ with $m > 1$, there is no number in $S$ which is a factor of $m$.
F for some (positive) factor $m$ of $n$ with $m > 1$, every number in $S$ is a factor of $m$.