1. True or False: If U is a subspace of V, and V is a subspace of W, U is a subspace of W. If true give proof of answer, if false, give an example disproving the statement. 2. My thoughts: If U is a subspace of V, then the zero vector is in V. As well as x+v is in V and ax is in V (by definition of a subspace). If these three are in V, and V is in W, then these three must be in W as well. Therefore U will be a subspace of W. However, I don't know if there is an example to disprove this, or if my logic is completely flawed. Thanks for any help!