Notating Sample Space of X, Y

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I need to show the sample space for the following: $$0 < x < 1$$

and

$$-1 < y < 1$$

On a graph, the area would look like the area shared in red. Is this correct? If so, how would I express the sample space in mathematical notation? I'm told it's the total area anywhere either x or y can occur.

Graph of X and Y area

I haven't been able to find any concrete examples of such notation.