Relation of Ideas vs Matter of Fact

In section four Hume talks about the distinction between "relations of ideas" and "matter of fact". According to Hume relations of ideas are a prior knowledge. These type of things would include all logical statments like all "men are batcholors" and 6+6=12. He then goes on to say that relation of ideas are certain and can't be thought of different, if you were to it would be a contradiction. It like saying 2+2=5 or 2+2=chair we know that is wrong just by the simple idea of relations of ideas thus we know 2+2=4.
Hume then moves on to talking about "matters of fact" which deal with experience. Matters of fact are things like the sun is shining, it is going to storm tommarrow, these are things we learn posteriori. These are also things in which we do not fear because of contradiction. So if i were to say there is a clown outside, it is pretty easy for someone to go outside and see if there is or not and prove me wrong. Hume also talks about how we know matters of facts about things in which we have not observed through a process of cause and effect. I know that my friend is in France though i have not seen it myself, through a letter i can draw that conclusion.