instead of taking care of the duplicates in the query....let PHP do the work for you.
Put all the university info in 1 array, then use array_unique(), to remove the duplicates
$result = mysql_query("SELECT university_1, university_2, university_3 FROM stores WHERE status = 1 AND approved = 1");
while($row = mysql_fetch_array($result)) {
$u[] = stripslashes($row['university_1']); // ALL IN
$u[] = stripslashes($row['university_2']); // ONE
$u[] = stripslashes($row['university_3']); // ARRAY $u
}
$newU = array_unique($u); // remove duplicates from array
foreach($newU as $opts){
print '<option>'.$opts.'</option>';
}