I argued it as follows, let $p, q, r$ and $s$ be predicates
$p$: "$m$ is divisible by $k$"
$q$: "$k$ is divisible by $n$ ($n < k$ and $m$ is divisible by $n$) "
$r$: " $k$ is the smallest factor of $m$ other than $1$"
$s$: "$k$ is prime"
The true arguments: $(p \land r), (q\iff\lnot s), (r \implies\lnot q)$
$ p \land r $
$ r $
$ r \implies \lnot q $
$ \lnot q$
$q \iff \lnot s$
$ \therefore p \land r \implies s$ = If $k$ is the smallest factor of any integer $m, k$ is prime.
Is this correct?