Let $x,y,a,b$ be real numbers. For $x<y$ and $a<b$, show the cardinality of $[a,b]$ equals the cardinality of $[x,y]$.
I did the above problem, by defining a linear function as a bijection between the intervals. The next part of the problem states,
Extend your result (from above) to open and half-open intervals.
I'm just not sure what exactly I'm supposed to do next, the question seems vague. Am I supposed to show $(a,b)\sim (x,y)$? $[a,b]\sim (x,y)$? $[a,b)\sim (x,y]$?