Unselect or prevent selection of radio buttons based on current checked checkbox

For specific reasons, I have to have two separate divs for the two groups of checkbox (groups "I" and "II").  To pull them together, I've wrapped a "category" div class around the whole thing.  I apologize for the formatting of the html.

The idea is that I should only be able to check one checkbox in the whole structure.  If I didn't have two separate groups, that would not be an issue.  However, with my setup, I had to write some jquery to solve this problem.  I've attached the html and the jquery below.

I have the checkboxes working correctly.  However, this is an issue.  I can select the radio button B.1 even if checkbox A is selected.  This should not be allowed.  Likewise, I can select radio B.1. even if checkbox D is selected.  In other words, if a checkbox is selected, then all non-child radios (B.1, B.2, C.1, etc) should be cleared out.  As a bonus, it would be nice to actually hide those radio button groups if a a different checkbox is selected.  I should only be able to select radios if it's parent checkbox is selected.

Please check out my jquery and let me know how I can accomplish this.  I've tried many different approaches to no avail.

HTML:

<div class="category">
   <div>
      <div>
         <span><strong>I.</strong></span>
      </div>
   </div>
   <div>
      <div>&nbsp;</div>
      <div>
         <div id="skillsbox" maxselected="1">
            <div>
               <label for="skillsliteracy"><input class="" name="skills" id="skillsliteracy" value="literacy" type="checkbox"> A.</label>
            </div>
            <div>
               <label for="skillslogical"><input class="" name="skills" id="skillslogical" value="logical" type="checkbox"> B.</label>
               <span style="display: inline;" id="skillslogicaltogglebox">
                  <div id="skills_logicalbox">
                     <div>
                        <label for="skills_logicalskmath"><input class="" name="skills_logical" id="skills_logicalskmath" value="skmath" type="radio">B.1.</label>
                     </div>
                     <div>
                        <label for="skills_logicalskoth"><input class="" name="skills_logical" id="skills_logicalskoth" value="skoth" type="radio"> B.2.</label>
                     </div>
                  </div>
               </span>
            </div>
         </div>
      </div>
   </div>
   <div>
      <div>
         <span><strong>II.</strong></span>
      </div>
   </div>
   <div>
      <div>&nbsp;</div>
      <div>
         <div id="libstudbox" maxselected="1">
            <div>
               <label for="libstudliberal"><input name="libstud" id="libstudliberal" value="liberal" type="checkbox"> C.</label>

               <span style="display: inline;" id="libstudliberaltogglebox">
                  <div id="libstud_liberalbox">
                     <div>
                        <label for="libstud_liberallsmin"><input class="" name="libstud_liberal" id="libstud_liberallsmin" value="lsmin" type="radio"> C.1.</label>
                     </div>
                     <div>
                        <label for="libstud_liberallswom"><input class="" name="libstud_liberal" id="libstud_liberallswom" value="lswom" type="radio"> C.2.</label
                     </div>
                  </div>
               </span>
            </div>
            <div>
               <label for="libstudintl"><input name="libstud" id="libstudintl" value="intl" type="checkbox"> D.</label>
               <span style="display: inline;" id="libstudintltogglebox">
                  <div id="libstud_intlbox">
                     <div>
                       <label for="libstud_intllshist"><input class="" name="libstud_intl" id="libstud_intllshist" value="lshist" type="radio"> D.1.</label>
                     </div>
                     <div>
                        <label for="libstud_intllsglob"><input class="" name="libstud_intl" id="libstud_intllsglob" value="lsglob" type="radio"> D.2.</label>
                     </div>
                  </div>
               </span>
            </div>
            <div>
               <label for="libstudscience"><input name="libstud" id="libstudscience" value="science" type="checkbox"> E.</label>
               <span style="display: inline;" id="libstudsciencetogglebox">
                  <div id="libstud_sciencebox">
                     <div>
                        <label for="libstud_sciencelsnatsci"><input name="libstud_science" id="libstud_sciencelsnatsci" value="lsnatsci" type="radio"> E.1.</label>
                     </div>
                     <div>
                        <label for="libstud_sciencelstech"><input name="libstud_science" id="libstud_sciencelstech" value="lstech" type="radio"> E.2.</label>
                     </div>
                  </div>
               </span>
            </div>
         </div>
      </div>
   </div>
</div>

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jQuery:

$(function () {
    $(".category").find("input:checkbox").click(function () {
        var curr = $(this).is(":checked");
        $(".category input:checked").removeAttr("checked");
        if (curr) {
            $(this).attr("checked", true);
        }
    });
});

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