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.
These are assumptions we can't make and, as you pointed out, Arsenal have this bad habit of not capitalising on the good fortune that comes their way.
I think the team needs a makeover. Are there any big signings on the horizon? Or will it stay pretty much the same as last season?