@[USERNAME]The union is not a subspace. The union is bigger than P or L so it definitely can't be a subspace of either of them. and by adding a vector from P with a vector from U you can get to a point that is neither in P nor in U or in other words by adding two points from P∪L you can get to points outside of P∪L (somewhere in R³). But to form a subspace you have to be able to add any vectors from that subspace and the result has to be in that subspace.####[]