\text { Consider the subset } 2^{n} c c^{n} \text { of points } a=\left(a_{1}, \ldots \ldots . . a_{n}\right) \text { where each a } \in 2 \begin{aligned} &\text

{ a) Prove that if } \mathrm{f} \in \mathrm{c}\left\{x_{1} \ldots \ldots \ldots x_{\mathrm{n}}\right\} \text { is a polynomial which variable at all points a } \in 2^{\mathrm{n}}\\ &\operatorname{then} f=0 \end{aligned} \text { b) Prove that } 2^{\mathrm{n}} \text { is not an affine algebraic variety in } c^{\mathrm{n}}