examday

/TMUA

In this question, $a_1,\ldots,a_{100}$ and $b_1,\ldots,b_{100}$ and $c_1,\ldots,c_{100}$ are three sequences of integers such that

for each $n$.

Which of the following statements must be true?

• I. $\begin{aligned}(\text{minimum of }a_1,\ldots,a_{100})\le{}&(\text{minimum of }b_1,\ldots,b_{100})\\&+(\text{minimum of }c_1,\ldots,c_{100})\end{aligned}$
• II. $\begin{aligned}(\text{minimum of }a_1,\ldots,a_{100})\ge{}&(\text{minimum of }b_1,\ldots,b_{100})\\&+(\text{minimum of }c_1,\ldots,c_{100})\end{aligned}$
• III. $\begin{aligned}(\text{maximum of }a_1,\ldots,a_{100})\le{}&(\text{maximum of }b_1,\ldots,b_{100})\\&+(\text{maximum of }c_1,\ldots,c_{100})\end{aligned}$