php regex or | operator

I am doing a preg_replace:

$pattern = '/<ul>/';
$replacement = "";
$string = "hello <ul> how are you doing </ul>";
echo preg_replace($pattern, $replacement, $string);

That will replace my <ul> with "" but Id like to replace anything that is a <ul> or </ul>, I am not getting how to use the | (or) character though.

I try like this, but it is not working right:

$pattern = '/<ul>|</ul>/';
$replacement = "";
$string = "hello <ul> how are you doing </ul>";
echo preg_replace($pattern, $replacement, $string);

Any help would be surely appreciated

Thanks, Bryan