How to prove that any integer n which is not divisible by 2 or 3 is not divisible by 6?
The point was to prove separately inverse, converse and contrapositive statements of the given statement: "for all integers n, if n is divisible by 6, then n is divisible by 3 and n is divisible by 2".
I have the proof for converse and inverse similar to that given in comments.
I have trouble only with the proof that integer not divisible by 2 or 3 is not divisible by 6.
As I review my proof for inverse statement, I'm not sure of it as well. "For all integers n, if n is not divisible by 6, n is not divisible by 3 or n is not divisible by 2."
n = 6*x where x in not an integer
n = 2*3*x
n/2 = 3*x and n/3 = 2*x where 2x or 3x is not an integer,
so n is not divisible by 2 or 3
Best Answer
If $6\mid n$, then $n=6\cdot k$ for some $k$. So $n=2\cdot 3\cdot k$. Thus $n$ is divisible by $2$ and $3$.