How can I display show/hide elements when user is registered?

There is no way to do this based on registered vs unregistered status because all users are anonymous until they log in. If you mean “logged in” vs “not logged in” then …

if (is_user_logged_in()) {
  // logged in content
} else {
  // not logged in content
}

Reference:

http://codex.wordpress.org/Function_Reference/is_user_logged_in

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