Alternatively, you can use bit operations rather than simple incrementation to encode a little extra info. The FAQ code structure is more immediately obvious, but this may do more of what you want:

#!/usr/bin/perl
use strict;
use warnings;

my $master = shift;
my $completed = shift;

open my $mh, '<', $master or die "Open fail on $master: $!";
my @master_lines = <$mh>;
chomp @master_lines;

open my $ch, '<', $completed or die "Open fail on $completed: $!";
my @completed_lines = <$ch>;
chomp @completed_lines;

my %count;

for my $element (@master_lines) {
    $count{$element}|=1;
}
for my $element (@completed_lines) {
    $count{$element}|=2;
}

print "$master only:\n";
for my $element (@master_lines) {
    next if $count{$element} & 2;
    print "$element\n";
}

print "$completed only:\n";
for my $element (@completed_lines) {
    next if $count{$element} & 1;
    print "$element\n";
}
[download]

There are already several tools to achieve what you want, writing your own is probably needless.

$ diff <( sort master ) <( sort completed ) | grep '^<' | cut -d ' ' -
+f2-
[download]

Depending on your needs you may want to use sort -u instead of a simple sort.

Or if you're under some Debian-derivative distro just install the moreutils package and use combine:

$ combine master not completed 
1ao8A
1jkxA
1juvA
1mejA
1meoA
1n0uA
1pjqA
[download]

Hope that helps.

I often use comm instead of diff, too.