a$)$ Give a context$-$free grammar for the language $A$ of strings over $\{x,y\}$ that are formed from a sequence of $x\text{'}$s followed by a sequence of $y^{\text{'}}$ s$,$ such that there are always the same number of $x\text{'}$s as $y\text{'}$s or else one more $x$ than $y.$ Examples: $,x,xy,y,$ xxyy$.$ Is your grammar ambiguous? Why or why not?

b$)$ Give a context$-$free grammar for the language $B$ of strings over $\{x,y\}$ that are formed from at most one occurrence of $y$ and any number of $x^{\text{'}}s.$ Examples: $,y,x,xy,yx,,xyx,y,x.$ Is your grammar ambiguous? Why or why not?

c$)$ Give a context$-$free grammar for the language $C$ over $\{x,y\}$ in which the string is a concatenation for two strings such that the first string is in $A($from Part a$)$ and the second string is in $B($from Part b$).$ Is your grammar ambiguous? Why or why not

d$)$ Draw all possible parse trees for the strings xxxyyy and xxyyxx using your grammar from Part c$.$