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In each of the following, determine if the given set is a subspace or not. For each case in which the set is a subspace, verify that it is a subspace by showing that subspace properties (S0), (S1), and (S2) hold. For each case in which the set is not a subspace, state one of the properties of a subspace that does not hold (either (S0), (S1), or (S2)) and give a counterexample showing that the property fails. U=\left\{\left[\begin{array}{c}

w \\

x \\

y \\

z

\end{array}\right] \in \mathbb{R}^{4} \mid 2 x-5 z=0 \text { and } w+y=0\right\} V=\left\{\left[\begin{array}{l}

x \\

y

\end{array}\right] \in \mathbb{R}^{2} \mid x-y \in \mathbb{Z}\right\} W=\left\{\left[\begin{array}{l}

x \\

y \\

z

\end{array}\right] \in \mathbb{R}^{3}|| x-z|=| y-z \mid\right\}

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