$W$ a subset of $\mathbb{R}^5$ consisting of all vectors an odd number of the entries in which are equal to $0$. Is $W$ a subspace of $\mathbb{R}^5$? Let $W$ be the subset of $\mathbb{R}^5$ consisting of all vectors an odd number of the entries in which are equal to $0$. Is $W$ a subspace of $\mathbb{R}^5$?
I'm not sure how to do this. Any solutions or hints are greatly appreciated. I know that in order for anything to be a subspace of something the zero vector must be in it. How would I go about this? What exactly do we mean by subset here? Is it any $5$-tuple or could it be $1,2,3,4,5$-tuples?

No. For instance, let $v=(0,1,1,1,1)$ and $w=(1,0,1,1,1)$. Then $v,w\in W$ but $v+w=(1,1,2,2,2)\notin W$.
