Hey!!!
I want to show that if $I,J$ are ideals of $K[x_1, x_2, \dots , x_n]$, then it stands that $V(I \cap J)=V(I) \cup V(J)$.
To show the inclusion $\subseteq$ I started like that:
Let $x \in V(I \cap J)$. That means that $\forall f \in I \cap J : f(x)=0$
But... how could we continue?