I am working on the exercise where the hypothesis is : Let $X$ be a scheme such that there exists affine open subsets $U_i \ (1 \leq i \leq n)$ such that $X = \cup U_i$. Further any two of the $U_i$'s have intersection which can be covered by a finite number of affine open subsets.
Suppose I take $U_i \cap U_j$. Does this mean $U_i \cap U_j \subseteq V_1 \cup ... \cup V_m$ or $U_i \cap U_j = V_1 \cup ... \cup V_m$, where each $V_j$ is an affine open subset? (I was also wondering if they were equivalent statemetns?) Thanks!