# Thread: subset U subset is NOT subspace of Superset?

1. ## subset U subset is NOT subspace of Superset?

Hello,
I have an assignment due tomorrow, and Im stuck at this problem:

Let V be a vector space over any field F, and W1 and W2 be two subspaces of V.
b) Give examples for V, W1, W2 such that W1 U W2 is NOT a subspace of V.

Any ideas?

2. In $\mathbb{R}^2$ : $span\{(1,0)\} \cup span\{(0,1)\}$ is not a subspace - for instance it does not contain $(1,0)+(0,1)$