Hi, I have this problem that is solved, but I don't understand the theory behind it. It says: Which of the following sets, with the natural definitions of addition and scalar multiplication, form real vector spaces? A) The set of all differentiable functions [itex]f:(0,1)\rightarrow\Re[/itex] such that [itex]f+f'=0[/itex]. B) The set of all differentiable functions [itex]f:(-1,1)\rightarrow\Re[/itex] such that [itex]f+f'=0[/itex] and [itex]f(0)=1[/itex]. The answer says the first one is a vector space, but that the second one is not because zero does not belong to the set... However, I don't see the reasoning behind it. Maybe they are supposed to be the opposite (A is not a vector space and B is) and the answer is wrong? No one has complained about it and there is nothing on the course forum, so I think the answers should be correct :/ Thanks a lot!