3 10 points a prove that the union of the three coordinate axes in the
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3. (10 points) (a) Prove that the union of the three coordinate axes in the 3-space is an affine algebraic variety. \text { (b) Prove that } \mathbf{R}^{2} \backslash\{(x, 0):
x \in \mathbf{R}\} \text { is not an algebraic variety. }