Liverpool beating Arsenal doesn't mean anything in the grand scheme of things for the short term, because lets be honest Liverpool will lose a game too, it's possible for them to go unbeaten but I doubt it, they will lose, and Arsenal can cover that difference.
That assumes Arsenal will win whenever Liverpool loses. I think last season or the season before that shows that Arsenal struggle to close the gap when it matters. They need to win every game to make sure they can win the title. Being complacent and believing that your competitor will slip up because you did is not really good. That being said, I think this applies to every team, not necessarily Arsenal only.