--- a/handouts/ho02.tex	Fri Sep 25 17:39:02 2015 +0100
+++ b/handouts/ho02.tex	Fri Sep 25 20:59:24 2015 +0100
@@ -233,7 +233,7 @@
 The other function of our matching algorithm calculates a
 \emph{derivative} of a regular expression. This is a function
 which will take a regular expression, say $r$, and a
-character, say $c$, as argument and return a new regular
+character, say $c$, as argument and returns a new regular
 expression. Be careful that the intuition behind this function
 is not so easy to grasp on first reading. Essentially this
 function solves the following problem: if $r$ can match a
@@ -271,7 +271,7 @@
 straightforward: all strings of the form $c\!::\!s$ are either
 matched by the regular expression $r_1$ or $r_2$. So we just
 have to recursively call $der$ with these two regular
-expressions and compose the results again with $+$. Yes, makes
+expressions and compose the results again with $+$. Makes
 sense? The $\cdot$-case is more complicated: if $r_1\cdot r_2$
 matches a string of the form $c\!::\!s$, then the first part
 must be matched by $r_1$. Consequently, it makes sense to
@@ -332,7 +332,7 @@
 Step 4: & the string is exhausted; test & ($nullable(r_4)$)\\
         & whether $r_4$ can recognise the\\
         & empty string\smallskip\\
-Output: & result of the test $\Rightarrow true \,\text{or}\, \textit{false}$\\        
+Output: & result of this test $\Rightarrow true \,\text{or}\, \textit{false}$\\        
 \end{tabular}
 \end{center}