Let $R$ be a ring and $X_1,X_2 \subseteq \mathbb{A}^n$ two algebraic sets such that $X_1 \subseteq X_2$. Then is it true that $I(X_1) \supseteq I(X_2)$ where
$$I(X) = \{f \in R \, | \, f(p)=0 \, \, , \, p \in X\} $$
If $f \in I(X_1)$ then $f(p)=0 \, \, \, \forall p \in X_1$ but if $p \in X_1 \Rightarrow p \in X_2$ and so I would rather think that $I(X_1) \subseteq I(X_2)$