Easy# Associativity Inheritence

LINALG-3VKOGT

If $V$ is a real vector space and $W\subseteq V$ has the property that for each $\vec{w}\in W$ one has $c\vec{w}\in W$ for each $c\in\mathbb{R}$ and for:

$$\vec{w}_1,\ \vec{w}_2\in W$$

...one has:

$$\vec{w}_1-\vec{w}_2\in W$$

...then which of the following is *FALSE*.