Cleanup

Advanced/Definable Sets/parts/0 logic.tex

@@ -1,8 +1,9 @@
 \section{Logical Algebra}
 
 \definition{}
-Odds are, you are familiar with \textit{logical symbols}. \par
-In this handout, we'll use the following:
+\textit{Logical operators} operate on the values $\{\text{True}, \text{False}\}$, \par
+just like algebraic operators operate on numbers. \par
+In this handout, we'll use the following operators:
 \begin{itemize}
 	\item $\lnot$: not
 	\item $\land$: and
@@ -66,11 +67,15 @@ $\lnot A$ is the opposite of $A$, which is why it looks like a \say{negative} si
 \vspace{2mm}
 
 $A \rightarrow B$ is a bit harder to understand. Read aloud, this is \say{$A$ implies $B$.} \par
-The only time $\rightarrow$ is false is when $T \rightarrow F$. This may seem counterintuitive, but it makes sense. Think about it. \par
+The only time $\rightarrow$ is false is when $T \rightarrow F$. This may seem counterintuitive, but it will make more sense as we progress through this handout.
 
 \problem{}
 Evaluate the following.
 \begin{itemize}
+	\item $\lnot T$
+	\item $F \lor T$
+	\item $T \land T$
+	\item $(T \land F) \lor T$
 	\item $(T \land F) \lor T$
 	\item $(\lnot (F \lor \lnot T) ) \rightarrow T$
 	\item $(F \rightarrow T) \rightarrow (\lnot F \lor \lnot T)$
@@ -110,7 +115,7 @@ Evaluate the following.
 
 \problem{}
 Show that $\lnot (A \rightarrow \lnot B)$ is equivalent to $A \land B$. \par
-That is, show that these give the same result for the same $A$ and $B$.
+That is, show that these give the same result for the same $A$ and $B$. \par
 \hint{Use a truth table}
 
 \vfill