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

$$a _ { n } \leq b _ { n } + c _ { n }$$

for each $n$.\\
Which of the following statements must be true?\\
I (minimum of $\left. a _ { 1 } , \ldots , a _ { 100 } \right) \leq$ (minimum of $\left. b _ { 1 } , \ldots , b _ { 100 } \right) + \left( \right.$ minimum of $\left. c _ { 1 } , \ldots , c _ { 100 } \right)$\\
II (minimum of $\left. a _ { 1 } , \ldots , a _ { 100 } \right) \geq$ (minimum of $\left. b _ { 1 } , \ldots , b _ { 100 } \right) +$ (minimum of $c _ { 1 } , \ldots , c _ { 100 }$ )\\
III (maximum of $\left. a _ { 1 } , \ldots , a _ { 100 } \right) \leq$ (maximum of $\left. b _ { 1 } , \ldots , b _ { 100 } \right) +$ (maximum of $c _ { 1 } , \ldots , c _ { 100 }$ )

A none of them\\
B I only\\
C II only\\
D III only\\
E I and II only\\
F I and III only\\
G II and III only\\
H I, II and III