Evaluating supremum and infinum I have no verified solution for this question.
I had a few questions regarding this:
$X = [1,3]$
$Y = (1,3]$
$X-Y = \{ x-y| x\in X, y\in Y\}$
The two questions that I have are that:
$a)$ Find the value of: $X-Y$.
$b)$ Are $\sup(X-Y)$ and $\inf(X-Y)$ elements of $X-Y$?
Firstly is the answer to $a)$ Simply; $1-1=0, 3-3=0\Rightarrow X-Y= (0,0]$
And for $b)$ I have: $\sup(X)=1, \inf(X)=3$. And $\sup(Y)=3, \inf(Y)$ not possible.
$\sup(X-Y) = 1-3 = -2$
$\inf(X-Y)$ not possible.
If anyone has any feedback it would be greatly appreciated.

The solution is [-2,2) let me know if you need further clarification.
