I need to allow my users to set the default page of the blog. So when someone visits, "www.example.com/blog/" the page they see is either the blog posts list or a specific page.

It looks like I can tell which page is already set using:

get_option( 'page_on_front' ): returns the ID of the static page assigned to the front page. 

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Can I change that by using:

set_option( 'page_on_front', 10 );

How would I remove a specific front page that has already been set? Do I set it to null?

UPDATE:

I found this call to check if showing blog posts:

get_option( 'show_on_front' ) == 'posts';

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