Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 25I / i / Solution

A point $p$ belongs to $V(I_1+I_2)$ exactly when every polynomial $f_1+f_2$, with $f_j\in I_j$, vanishes at $p$. This implies that every member of each ideal vanishes by taking the other summand to be zero, and the converse follows by addition. HenceThis is the first vanishing loci of ideal sums and intersections identity.

Solved by gpt-5.6-sol high.