fix typos

Author: oscarlevin

source/ch_structures.ptx

@@ -5,7 +5,7 @@
 
   <introduction>
     <p>
-      Throughout the previous chapters, we have seen many examples of discrete structures and their properties and uses.  The following sections are  self-contained overviews of each of the main structures we have explored. These can either be studied prior to other material in the book, or as a review and reference after the fact. 
+      Throughout the previous chapters, we have seen many examples of discrete structures and their properties and uses.  The following sections are  self-contained overviews of each of the main structures we have explored. These can either be studied prior to other material in the book or as a review and reference after the fact. 
     </p>
   </introduction>
 

source/exercises/addtops-numbth.ptx

@@ -223,7 +223,7 @@
   <exercise>
     <statement>
       <p>
-        Solve the following congruence <m>5x + 8 \equiv 11 \pmod{22}</m>.  That is, describe the general solution.
+        Solve the congruence: <m>5x + 8 \equiv 11 \pmod{22}</m>.  That is, describe the general solution.
       </p>
 
     </statement>

source/exercises/intro-sets.ptx

@@ -729,11 +729,11 @@ $ans3 = 12;
   <exercise>
     <statement>
       <p>
-        Let <m>A</m>, <m>B</m> and <m>C</m> be sets. <ol>
+        Let <m>A</m>, <m>B</m>, and <m>C</m> be sets. <ol>
           <li>
             <p> Suppose that <m>A \subseteq B</m> and <m>B \subseteq C</m>.
-        Does this mean that <m>A \subseteq C</m>? Prove your answer. Hint: to prove that <m>A \subseteq C</m>
-        you must prove the implication, <q>for all <m>x</m>, if <m>x \in A</m> then <m>x \in C</m>.</q>
+        Does this mean that <m>A \subseteq C</m>? Prove your answer. Hint: To prove that <m>A \subseteq C</m>,
+        you must prove the implication, <q>For all <m>x</m>, if <m>x \in A</m>, then <m>x \in C</m>.</q>
             </p>
           </li>
 
@@ -762,8 +762,8 @@ $ans3 = 12;
     <statement category="bonus">
       <p>
         Find an example of a set <m>A</m> with <m>|A| = 3</m> which contains only other sets and has the
-        following property: for all sets <m>B \in A</m>, we also have <m>B \subseteq A</m>. Explain why
-        your example works. (FYI: sets that have this property are called <term>transitive</term>.) <idx><h>transitive
+        following property: For all sets <m>B \in A</m>, we also have <m>B \subseteq A</m>. Explain why
+        your example works. (FYI: Sets that have this property are called <term>transitive</term>.) <idx><h>transitive
         sets</h>
         </idx>
       </p>