JSFiddle - React, Tailwind, and code Playground

HTML

<form class="date_catcher">
    <div style="display:inline;" class="start">
        <select class='input-small month' name='month'>
            <option value='' selected='selected'>---</option>
            <option value='0'>Jan</option>
        </select>
        <select class='input-small year' name='year'>
            <option value='' selected='selected'>----</option>
            <option value="2012">2012</option>
        </select>
    </div>
    <div style="display:inline;" class="end">
        <select class='input-small month' name='month'>
            <option value='' selected='selected'>---</option>
            <option value='0'>Jan</option>
        </select>
        <select class='input-small year' name='year'>
            <option value='' selected='selected'>----</option>
            <option value="2012">2012</option>
        </select>
    </div>
</form>

JavaScript

$('.month, .year').change(function () {
    var $this = $(this);
   var $empty = $this.closest('form').find('.month, .year').filter(function(){
  return this.value === "";
}).length;
    if ($empty === 0) {
        console.log('there are no empty dropdowns');
    }
});