Write WP Query that selects posts that are part of the same two categories

by

There is a simple way using a default argument…

/*
* You need to get the IDs for the Categories you wish to include
*/
$args = array(
    'category__and' => array( 1, 3 )
);

$the_query = new WP_Query( $args );

if ( $the_query->have_posts() ) 
{
    // Do something to display your posts
    ...
} else 
{
    // no posts
}

wp_reset_postdata();