Remove “Comments are closed” Notice from Custom Post Type template

I’ve created a custom post type single template. I noticed that when I turn off comments, I get a notice that says “Comments are closed.”

Looking at my comments.php, I get this little bit of code:

     <?php else : // or, if we don't have comments:

        /* If there are no comments and comments are closed,
         * let's leave a little note, shall we?
         * But only on posts! We don't want the note on pages.
         */
        if ( ! comments_open() && ! is_page() ) :
        ?>
        <p class="nocomments"><?php _e( 'Comments are closed.', 'dukatheme' ); ?></p>
        <?php endif; // end ! comments_open() && ! is_page() ?>

This code makes it such that the notice is not shown on pages. How can I edit it to make sure it is not shown on pages AND my custom post type?

My custom post type is named “duka”.

Thanks!

Add a post type check to the if clause;

if ( ! comments_open() && ! is_page() && 'duka' != get_post_type() ) :