Originally Posted by

**slevvio** Hello, I was wondering if someone could give me a hint about where to start with the following problem. Any help would be appreciated.

(definitions)

Let $\displaystyle k$ be an algebraically closed field. Then let $\displaystyle J,J' \subseteq k[x_1,\ldots,x_n]$ be ideals. Then let $\displaystyle X = V(J), X' = V(J')$, i.e. algebraic sets. The ideal of $\displaystyle X $is $\displaystyle I_X := \{ f \in k[x_1 ,\ldots, x_n] | f(x) = 0 \forall x \in X\}$.

(problem)

give an example to show that $\displaystyle I_{X \cap X'} \not= I_X + I_{X'}$