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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:

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

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

...then which of the following is FALSE.


$\vec{0}\in W$


$W$ is closed under addition


$W$ is closed under addition but the addition fails to be associative


There are $\vec{w}$ in $W$ such that $-\vec{w}$ is not in $W$

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