Let $I_1$ and $I_2$ be homogenous ideals in $A:=\mathbb{C}[X_0,\ldots,X_n]$. Assume that $I_1 \subset I_2$. Let $X=\mathrm{Proj} (A/I_1)$ and $Y=\mathrm{Proj}(A/I_2)$. Then,
1) Is it true that the natural morphism $\Gamma(X,\mathcal{O}_X(n)) \to \Gamma(Y,\mathcal{O}_Y(n))$ is surjective?
2) Is it true that $\Gamma(X,\mathcal{O}_X(n))$ is isomorphic to the degree $n$ graded piece in $A/I_1$?