Remove "checked" from radio when a checkbox is unchecked

I have a checkbox (#FBmngCH) that reveals a set of radio buttons (name=adManage) when clicked. When the checkbox is unclicked, the radio button that was previously selected still remains checked. I would like to have the checked status of the radio button removed once the checkbox is unchecked.

This is being used in a form, so if the user changes their mind about selecting that service, I would like the details about that service to be wiped also (so the value of the selected radio will not end up in the PHP and ultimately the email). I hope this makes sense.

I have given this some considerable time and am not seeming to get this to work correctly. The last set of if-statements is the part of the code that I wrote. Not sure if I am missing something, selecting something wrong, or what. Any help with this would be highly appreciated. Thanks!

HTML

<li>
    <input type="checkbox" class="cbox" name="FBchecks[]" value="Facebook Ad MGMT" id="FBmngCH">
    <label for="test">Facebook Ad Management</label>
    <ul id="FBmngList">
        <li>
            <input type="radio" name="adManage" value="Ad Management 1" id="adMan1">
            <label for="adMan1">Ad Fund - 1</label>
        </li>
        <li>
            <input type="radio" name="adManage" value="Ad Management 2" id="adMan2">
            <label for="adMan2">Ad Fund - 2</label>
        </li>
        <li>
            <input type="radio" name="adManage" value="Ad Management 3" id="adMan3">
            <label for="adMan3">Ad Fund - 3</label>
        </li>
        <li>
            <input type="radio" name="adManage" value="Ad Management 4" id="adMan4">
            <label for="adMan4">Ad Fund - 4</label>
        </li>
        <div id="FBADerror" class="acctError"></div>
    </ul>
</li>



JS

$FBmngCH = $("#FBmngCH");
$FBmngList = $("#FBmngList");

//hide FB Management List
$FBmngList.hide();

//on FB Management select
$FBmngCH.click(function() {
    //toggle FB Management List
    $FBmngList.toggle();
});

$FBadValid = false;
$FBADerror = $("#FBADerror");

//if FB Ad Management is checked
if ($FBmngCH.attr('checked')) function validateFB() {
    $("input[name=adManage]").each(function () {   //LoopingthroughradioButtons
    // "this" is the current element(radio) in the loop
      if ($(this).is(':checked')) {
            $FBadValid = true; //Radio Button is Checked);
        }

      if ($FBadValid.attr = true ) {
            $FBADerror.empty();
        }
    });
};
  if ($FBmngCH.blur($FBadValid.attr = false)) {
        $FBADerror.append("<li> Please select a Facebook Ad plan. </li>");
        //appends error to document
    }   
    if ($FBmngCH.blur($FBmngCH.not('checked'))) {
        $("input[name=adManage]").each(function () {
            if ($(this).is(':checked')) {
                $("input[name=adManage]").removeAttr('checked');
            }
        });
        //remove checks from radios
    };  
$("input[name=adManage]").click(validateFB);