I have created a custom post type ‘book’. All book post-type are public, so I want to remove some capabilities such as ‘delete_private_books’, ‘read_private_books’ etc. How can I achieve this since when I activate member plugin it show all default capabilities including the above mentioned which has nothing to do with my custom post type.

I have registered my post type book and added capabilities to it.

$labels = array(
  'name'               => _x( 'Books', 'post type general name' ),
  'singular_name'      => _x( 'Book', 'post type singular name' ),
  'menu_name'          => _x( 'Book', 'admin menu' ),
  'name_admin_bar'     => _x( 'Book', 'add new on admin bar' ),
  'add_new'            => _x( 'Add New', 'Book' ),
  'add_new_item'       => __( 'Add New Book' ),
  'new_item'           => __( 'New Books' ),
  'edit_item'          => __( 'Edit Books' ),
  'view_item'          => __( 'View Books' ),
  'all_items'          => __( 'Books' ),
  'search_items'       => __( 'Search Books' ),
  'parent_item_colon'  => __( 'Parent text:' ),
  'not_found'          => __( 'No Books found.' ),
  'not_found_in_trash' => __( 'No Books found in Trash.' )
);

$capabilities = array(
  'edit_post'              => 'edit_books',
  'read_post'              => 'read_books',
  'delete_post'            => 'delete_books',
  'edit_posts'             => 'edit_books',
  'edit_others_posts'      => 'edit_others_books',
  'publish_posts'          => 'publish_books',
  'read_private_posts'     => 'read_private_books',
  'create_posts'           => 'edit_books',
  'delete_posts'           => 'delete_books',
  'delete_private_posts'   => 'delete_private_books',
  'delete_published_posts' => 'delete_published_books',
  'delete_others_posts'    => 'delete_others_books',
  'edit_private_posts'     => 'edit_private_books',
  'edit_published_posts'   => 'edit_published_books',
);
$args = array(
  'labels'             => $labels,
  'public'             => true,
  'publicly_queryable' => true,
  'show_ui'            => true,
  'show_in_menu'       => false,
  'query_var'          => true,
  'rewrite'            => array('slug' => 'books'),
  'capability_type'    => 'books',
  'has_archive'        => true,
  'hierarchical'       => false,
  'menu_position'      => '',
  'supports'           => false,
  'map_meta_cap'       => null,
  'capabilities'       => $capabilities,
);

register_post_type( 'wp-type-books', $args );