JSFiddle - React, Tailwind, and code Playground

HTML

<select name="SN" size="10" multiple="multiple">
<option value="150230">Абинск</option>
<option value="150277">Адлер</option>
<option value="150237">Адыгейск</option>
<option value="150238">Анапа</option>
<option value="150239">Армавир</option>
<option rel="Y" value="116613">Астрахань</option>
<option rel="Y" value="116614">Барнаул</option>
<option rel="Y" value="116615">Белгород</option>
<option rel="Y" value="116616">Брянск</option>
<option rel="Y" value="116617">Волгоград</option>
<option value="120080">Волжский</option>
<option rel="Y" value="116618">Воронеж</option>
<option value="150241">Геленджик</option>
<option value="150314">Георгиевск</option>
<option value="150256">Горячий Ключ</option>
</select>
<input type="text" id="log" name="log" value="" />

JavaScript

$("select[name='SN']").change(function () {
  if($("select[name='SN'] option:selected:[rel]=Y").length && 
    !$("select[name='SN'] option:selected:not([rel]=Y)").length){
     $('#log').val("есть");
  }else{
     $('#log').val("нет");
  }
});