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Directions: Show all the steps and write all the words of the proof, using the format shown in class. 1. Let \( W=\left\{\left[\begin{array}{l}p \\ q\end{array}\right]|p, q \in \mathbb{R}| p,|=| q \mid\right\} \). Prove, using a counter example, that the set \( \mathrm{W} \) is not closed under vector addition. 2. Let \( U=\left\{\left[\begin{array}{l}p \\ q \\ r\end{array}\right] \mid p, q, r \in \mathbb{R}, p+q+r=5\right\} \). By providing a counter example, prove... a) that \( U \) is not closed under scalar multiplication. b) that \( \mathrm{U} \) is not closed under vector addition.

1. We have [?11],[11]?W because