Is it possible to construct a NOT gate if given only OR gates and XOR gates?
Yes it's possible. Virtually any gate is possible so long as you have a 2 input gate with the capability for inversion.

Take a closer look at an XOR gate truth table and you should be able to see how to do it:

\begin{array} {|c|c|c|}
\hline A &amp; B &amp; OUT \\
\hline 0 &amp; 0 &amp; 0 \\  
\hline 0 &amp; 1 &amp; 1 \\ 
\hline 1 &amp; 0 &amp; 1 \\
\hline 1 &amp; 1 &amp; 0 \\ 
\hline 
\end{array}

I'll give you just the opposite of what you want even to show you how it works:
Set B to 0 and what do you get?  

\begin{array} {|c|c|c|}
\hline A &amp; B &amp; OUT \\
\hline 0 &amp; 0 &amp;  0  \\
\hline 1 &amp; 0 &amp;  1  \\
\hline 
\end{array}
What'd that do to the truth table and A? It turned it into a pass/buffer gate. Whatever comes in A is exactly what comes out.