$X = [1,3]$

$Y = (1,3]$

Given that:

$\begin{align} X - Y = [-2;2) \end{align}$

(Thanks to Graham Kemp for helping me with this - I have asked a similar question before, but had no responses.)

Are $\sup(X-Y)$ and $\inf(X-Y)$ elements of $X-Y$?

I have that:

inf(X) = 1 and sup(X) = 3

Then:

inf(Y) = 1 and sup(Y) = 3

inf(X-Y) = inf X - sup Y = 1 - 3 = -2
sup(X-Y) = sup X - inf Y = 3 - 1 = 2

So to solve my question - I have:

Since inf(X-Y) = -2 and sup(X-Y) = 2. Then from the interval notation 2 is not bounded in the interval notation, whereas -2 is. So then inf(X-Y) is an element of X-Y and sup(X-Y) is not an element of X-Y. 

I want to ask if this is correct.
Thank you