Let $I=(xy, xz, yz)$ be an ideal of $\mathbb{C}[x,y,z]$.
Prove that $I$ cannot be generated by $2$ elements.
2. Is it possible to generate the element $xy+xz+yz$ with only two of those elements?
Is it possible to generate the element $xy+xz+yz$ with only two of those elements?
i think you misunderstood the question! the claim is that it's not possible that two elements of $I=(xy,xz,yz)$ generate $I.$