Write a script cmprpaths that compares the directories specified in CDPATH and PATH, reporting on any that don't appear in both. For example, if

PATH="/bin:/usr/bin/:$HOME/bin"
CDPATH="$HOME/bin:$HOME/projects"

Then the program would report:
$ cmprpaths
/bin appears only in PATH
/usr/bin/appears only in PATH
$HOME/projects appears only in CDPATH
$

There are a number of solutions for this particular script. I took the brute force approach, comparing each of the PATH values to all CDPATH values, then vice versa. There are more efficient solutions too, of course, and changing IFS to ":" also helps ensure that directories with spaces in their path work properly. But that's in Chapter 11.
for pathdir in $( echo $PAT | sed 's/:/ /g')
do
match=0
for cdpathdir in $( echo $CDP | sed 's/:/ /g')
do
if [ "$cdpathdir" = "$pathdir" ] ; then
match=1
fi
done
if [ $match -eq 0 ] ; then
echo "$pathdir appears only in PATH"
fi
done

## then we do the same thing, but with the two variables swapped

for cdpathdir in $( echo $CDP | sed 's/:/ /g')
do
match=0
for pathdir in $( echo $PAT | sed 's/:/ /g')
do
if [ "$cdpathdir" = "$pathdir" ] ; then
match=1
fi
done
if [ $match -eq 0 ] ; then
echo "$cdpathdir appears only in CDPATH"
fi
done