Automatically check a checkbox if a group of others are not checked

I'm a librarian working on improving my library's main search feature. I am trying to get a checkbox labeled "Everything" to check automatically if users deselect all of the other options ("books," "articles," "music," "videos".)

Here's the relevant javascript:

$(document).ready(function() {
var $others = $('input[class="checkoption"]').not('#everythingbox')
$others.change(function() {
if (this.checked==false) {
$('#everythingbox').prop('checked', true)
}
});
});

I almost have it working, but there's a problem: if I select two or more choices and deselect one, "Everything" checks automatically, but I only want it to check automatically if none of the others are checked.

Here is the full fiddle: http://ift.tt/2Bco5hW

Any advice would be very much appreciated!