Let W1 and W2 be subspaces of a vector space V. Prove that W1[itex]\bigcup[/itex]W2 is a subspace of V if and only if W1[itex]\subseteq[/itex]W2 or W2[itex]\subseteq[/itex]W1 Well so far, I have proven half of the statement (starting with the latter conditions). Right now I'm struggling to show that the final conditions follow from W1[itex]\bigcup[/itex]W2. I have an idea for the method: assume that W1[itex]\subseteq[/itex]W2 is not true, and then prove that W2[itex]\subseteq[/itex]W1 must follow. This is my first linear algebra class, and this is from the first problem set due, so I know that nothing that complex is going on here. However, I've been looking at this problem for the past 30 minutes or so, and I'm hoping that someone could push me in the right direction.