Mockingbird edits

Advanced/Mock a Mockingbird/parts/00 intro.tex

@@ -8,7 +8,7 @@ Bird $AB$ is, by definition, $A$'s response to $B$.
 
 As you wander around this forest, you quickly discover two interesting facts:
 \begin{enumerate}[itemsep = 1mm]
-	\item $A$'s responds to $B$ mustn't be the same as $B$'s response to $A$.
+	\item $A$'s response to $B$ mustn't be the same as $B$'s response to $A$.
 	\item Given three birds $A$, $B$, and $C$, $(AB)C$ and $A(BC)$ are not necessarily the same bird. \\
 	Bird $A(BC)$ is $A$'s response to bird $BC$, while $(AB)C$ is $AB$'s response to $C$. \\
 	Thus, $ABC$ is ambiguous. Parenthesis are mandatory.

Advanced/Mock a Mockingbird/parts/01 tmam.tex

@@ -29,7 +29,7 @@ Complete his proof.
 
 \vfill
 \problem{}
-We say a bird $A$ is \textit{egocentric} if it is fond if itself. \\
+We say a bird $A$ is \textit{egocentric} if it is fond of itself. \\
 Show that the laws of the forest guarantee that at least one bird is egocentric.
 
 
@@ -56,7 +56,7 @@ Show that the laws of the forest guarantee that at least one bird is egocentric.
 
 \definition{}
 We say a bird $A$ is \textit{agreeable} if for all birds $B$, there is at least one bird $x$ on which $A$ and $B$ agree. \\
-In other words, $A$ is agreeable if $Ax = Bx$ for some $x$ for all $B$.
+In other words, $A$ is agreeable if given any $B$, we can find a bird $x$ satisfying $Ax = Bx$.
 
 \problem{}
 Is the Mockingbird agreeable?
@@ -71,7 +71,7 @@ Is the Mockingbird agreeable?
 
 \problem{}
 Take two birds $A$ and $B$. Let $C$ be their composition. \\
-Show that $A$ must be agreeable if $C$ is agreeable.
+Show that if $C$ is agreeable, $A$ is agreeable.
 \begin{alltt}
 	\cmnt{Given information}
 	let A, B
@@ -125,9 +125,11 @@ Given three arbitrary birds $A$, $B$, and $C$, show that there exists a bird $D$
 \vfill
 
 
-\problem{}
+\definition{}
 We say two birds $A$ and $B$ are \textit{compatible} if there are birds $x$ and $y$ so that $Ax = y$ and $By = x$. \\
 Note that $x$ and $y$ may be the same bird. \\
+
+\problem{}
 Show that any two birds in this forest are compatible. \\
 \begin{alltt}
 	let A, B

Advanced/Mock a Mockingbird/parts/02 kestrel.tex

@@ -28,12 +28,12 @@ Say $A$ is fixated on $B$. Is $A$ fond of $B$?
 \definition{}
 The \textit{Kestrel} $K$ is defined by the following relationship:
 $$
-	(Kx)y = x
+	(Kx)y = x~~~\forall x, y
 $$
 In other words, this means that for every bird $x$, the bird $Kx$ is fixated on $x$.
 
 \problem{}
-Show that an egocenteric Kestrel is hopelessly egocentric
+Show that an egocenteric Kestrel is hopelessly egocentric.
 
 \begin{solution}
 	\begin{alltt}