jquery if checkbox is not selected

What is wrong in following jquery code ? If the menu which contains value 1 is selected, at least one submenu must be checked.

It is not working, if submenu is checked, still it alert message and is stopping. I am trying adding [name='submenu[]'] or storing value in variable but it doesn't work.

if ($("[name='menu[]']:checked").val() == 1) {
  if ($("[name='submenu[][]']:checked").length == 0) {
    alert('Select at least one submenu ');
    return false;
  }
}

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<ul>
  <li><input type="checkbox" name="menu[]" value="1">News
    <ul>
      <li><input type="checkbox" name="submenu[1][]" value="1">Local</li>
      <li><input type="checkbox" name="submenu[1][]" value="2">National</li>
    </ul>
  </li>
  <li><input type="checkbox" name="menu[]" value="2">Views</li>
  <li><input type="checkbox" name="menu[]" value="3">Comment</li>
</ul>