Trouble understanding how to create a grammar parse tree
Before expanding a grammar into a parse tree, we should first try to understand it at a higher level.

&lt;list&gt; -&gt; &lt;item&gt; , &lt;list&gt; | &lt;item&gt; 
&lt;item&gt; -&gt; &lt;left&gt; &lt;item&gt; &lt;right&gt; | &lt;left&gt; &lt;right&gt;
&lt;left&gt; -&gt; A| B | C 
&lt;right&gt; -&gt; x | y | z


First, &lt;list&gt; is a list of &lt;item&gt;, separated by commas if there are multiple ones.   

Second, an item is either a pair of alphabets (the left is one of A | B | C; the right is one of x | y | z) or recursively, an item surrounded by such a pair.
Thus, an &lt;item&gt; is a word composed of, say $n$, upper-case alphabets from A | B | C, followed by the same number, $n$, of lower-case alphabets from x | y | z.


  $Q_1$: Choose a string that is in this language and create a parse tree that demonstrates that your claim is true. 


ABCxyz,ACyz is in this language; can you generate a parse tree for it?


  $Q_2$: Identify another string that contains some of these terminals symbols but is not in the language.


AyCz is not in this language; can you explain why?



In addition, when you are searching for any string in a grammar by expanding the grammar into a parse tree, you can push the tree into its leaves as fast as you can, by choosing the non-recursive rules whenever possible.