No custom post types appearing in admin menu

I’m building my first plugin, and attempting to register three custom post types in my setup_post_types() function. Within that function, I’m using the register_post_type function, exactly as instructed in the codex (see code below). However, when I activate my plugin, the post types that I registered are not appearing anywhere. My entire plugin consists of one file right now, so what you see below is everything (minus the commented meta data for all plugins).

add_action( 'init', 'setup_post_types' );
function setup_post_types() {

    // Register our "appointment" custom post type
    $appt_labels = array(
        'name'               => __('Appointments'),
        'singular_name'      => __('Appointment'),
        'menu_name'          => __('My Appointments'),
        'name_admin_bar'     => __('New Appointment'),
        'all_items'          => __('View All Appointments'),
        'add_new'            => __('Book New Appointment'),
        'add_new_item'       => __('Book New Appointment'),
        'edit_item'          => __('Update Appointment'),
        'new_item'           => __('Book New Appointment'),
        'view_item'          => __('Preview this Appointment'),
        'search_items'       => __('Search My Appointments'),
        'not_found'          => __('No Appointments Found'),
        'not_found_in_trash' => __('No Appointments found in Trash')
    );
    $appt_args = array(
        'labels' => $appt_labels,
        'public' => 'true',
        'show_ui' => 'true',
        'show_in_menu' => 'true',
        'show_in_admin_bar' => 'true',
        'menu_position' => 23,
        'menu_icon' => 'dashicons-backup',
        'rewrite' => array('slug' => 'appts'),
        'has_archive' => true
    );

    register_post_type('whattimeagain_appt', $appt_args);

    // Register our "vendor" custom post type
    $vendor_labels = array(
        'name'               => __('Vendors'),
        'singular_name'      => __('Vendor'),
        'menu_name'          => __('My Vendors'),
        'name_admin_bar'     => __('Add Vendor'),
        'all_items'          => __('All Vendors'),
        'add_new'            => __('Add New Vendor'),
        'add_new_item'       => __('Add New Vendor'),
        'edit_item'          => __('Update Vendor Information'),
        'new_item'           => __('Add New Vendor'),
        'view_item'          => __('Preview Vendor Information'),
        'search_items'       => __('Search My Vendors'),
        'not_found'          => __('Vendor not Found'),
        'not_found_in_trash' => __('Vendor not found in Trash')
    );
    $vendor_args = array(
        'labels' => $vendor_labels,
        'public' => 'true' ,
        'show_ui' => 'true',
        'show_in_menu' => 'true',
        'show_in_admin_bar' => 'true',
        'menu_position' => 21,
        'menu_icon' => 'dashicons-businessman',
        'rewrite' => array('slug' => 'vendors'),
        'has_archive' => true
    );

    register_post_type('whattimeagain_vend', $vendor_args);

    // Register our "customer" custom post type
    $customer_labels = array(
        'name'               => __('Customers'),
        'singular_name'      => __('Customer'),
        'menu_name'          => __('My Customers'),
        'name_admin_bar'     => __('Add Customer'),
        'all_items'          => __('All Customers'),
        'add_new'            => __('Add New Customer'),
        'add_new_item'       => __('Add New Customer'),
        'edit_item'          => __('Update Customer Information'),
        'new_item'           => __('Add New Customer'),
        'view_item'          => __('Preview Customer Information'),
        'search_items'       => __('Search My Customers'),
        'not_found'          => __('Customer not Found'),
        'not_found_in_trash' => __('Customer not found in Trash')
    );
    $customer_args = array(
        'labels' => $customer_labels,
        'public' => 'true',
        'show_ui' => 'true',
        'show_in_menu' => 'true',
        'show_in_admin_bar' => 'true',
        'menu_position' => 22,
        'menu_icon' => 'dashicons-groups',
        'rewrite' => array('slug' => 'customers'),
        'has_archive' => true
    );

    register_post_type('whattimeagain_cust', $customer_args);

}
function activate() {

    // Trigger our function that registers the custom post type
    setup_post_types();

    // Clear the permalinks after the post type has been registered
    flush_rewrite_rules();

}
function deactivate() {

    // Our post type will be automatically removed, so no need to unregister it

    // Clear the permalinks to remove our post type's rules
    flush_rewrite_rules();

}

register_activation_hook(__FILE__,  'activate');
register_deactivation_hook(__FILE__,  'deactivate');