Read the two statements and choose the correct option.

I. On $[0, 1]$, $f(x) = x^{2}$ has greatest value 1.

II. On $(0, 1)$, $f(x) = x^{2}$ has a greatest value.

Explanation

1. 01

   I: $x^{2}$ rises on $[0, 1]$, so its greatest value is $f(1) = 1$. True.

2. 02

   II: on $(0, 1)$, $x^{2}$ comes as close to 1 as we like but never reaches it, so no value is the greatest. False.