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