We are told $P\implies Q$.
There are $4$ hypothetical possibilities.
- $P$ is not true and $Q$ is not true.
This could happen.
- $P$ is not true and $Q$ is true.
The could happen.
- $P$ is true and $Q$ is not true.
This can not happen. We we told $P\implies Q$ so if we have $P$ we must have $Q$ be true. This is just not possible.
- $P$ is tru and $Q$ is true.
Now in every single case where $P$ is true we had to have $Q$ also be true. So.... $Q$ is necessary for $P$.
but why can't I have P standalone?
Well, what does $Q$ do, while we have $P$ stand by itself? We can ignore $Q$ and not look at $Q$ but and we can choose to not invite $Q$ to our party, but we can't make $Q$ ... disappear. Now matter what we do with $P$, $Q$ is still going to exist and either be true or false even if you don't look at it.
So we have $P$ at our party and there it is... being true. That's fine but someone might wonder "Hmm, I wonder what $Q$ is doing" and everyone else can ignore $Q$ but, $Q$ will be sitting on the other side of the hill doing it's $Q$ thing of being true or false. So someone wonders over to check on $Q$ and what does she see?
Well, $P\implies Q$ so, lo and behold, $Q$ is being true. It doesn't matter if we look at $Q$. So long as $P\implies Q$ then if we ever have $P$, it will always be that $Q$ is true, whether we look at it or not.
And since every time $P$ is true, $Q$ is true, we can't have $P$ be true without $Q$ being true (even if we stick $Q$ is a little cottage three thousand miles away and pass a law that no-one is allowed to check in on him-- $Q$ will just sit there being true all by himself unnoticed and unloved), so $Q$ is necessary for $P$ to be true.