If statement for catergories

<?php

    $current_user = wp_get_current_user();

    if ( is_category( 'Cars' ) && 0 == $current_user->ID ) { ?>

<!-- HTML markup here -->

<?php } else { ?>

<!-- other HTML markup here -->

<?php } ?>

ID will be 0 in the $current_user object, if the user isn’t logged in.

Related reading:

• is_category
• wp_get_current_user

EDIT

Try using is_user_logged_in() and in_category() instead:

<?php
if ( in_category( 'cars' ) && ! is_user_logged_in() ) {
    // Current post is in the category 'cars'
    // and the current user is NOT logged in;
    // do something
} else {
    // do something else
}
?>