[Plugin: Widget Logic] Shortcode for a parent page and it child pages

I would like to know what is the shortcode to include a widget for a particular page like “product 1” and also to his child pages like “service A” + “service B” + “service C” + “service D”, etc…

Parent page + sub pages

There ise a way to do it automatically, because i use this shortcode :

is_page( array( 'product 1', 'service A', 'service B', 'service D', 'service E', 'service F', 'service G', 'service H', 'service I', 'service J', 'service K' ) ) AND MUCH MORE...

But imagine you have 10 pages of products, and each product have 15 dedicated pages of servicies…It become difficult to write correctly shortcodes..

There is an easier way to use shortcode than is_page( array ??

Thank you !

http://wordpress.org/extend/plugins/widget-logic/