A is closed and bounded subset of R. Which of the following exist? $\sup A$
$\inf A$
$\max A$
$\min A$
I Thought all of them exist! Since $\sup = \max$ and $\inf = \min$ if it's closed and bounded.
But the answer says otherwise. Why???
Can anyone please help? Thank you.

Trick question! The empty set is closed and bounded. (You are right for non-empty sets.)
Remark: It is a matter of taste whether the infimum and supremum of the empty set exist. Some people define the infimum to be $\infty$ and the supremum to be $-\infty$ (There is no typo in the previous sentence!) But definitely the max and min of the empty set do not exist.
