The only reading on vacuous truth has been from Wikipedia, so I may be misunderstanding something here. Anyway, I was skimming through a Linear Algebra textbook and it said that the empty set is NOT a subspace of every vector space. But I was thinking, shouldn't this be vacuously true? For example, one of the conditions that a set must meet in order for it to be a vector space is that given two elements of the set x and y, x + y = y + x. Isn't this vacuously true for the empty set because there are no elements in the set at all?