JQuery :: Treating Two Sets Of Radio Button Groups As One?

I have a situation where within my form I establish two different sets of radio button groups. The real world example field group names are "Mens" and "Womens".

Everything works fine with my form until the user submits the form but then selects their browsers "back" button. When they are returned back to their product page from their cart their previous selection remains active. If the user then selects an option from the second set of radio buttons their submission contains both selections which I do not want.

I can clear all of the radio button states with the following function just after the form is submitted:

Code JavaScript:
$(".cart input:radio").click(function(){
$(this).parent().submit();
this.checked = false;
});

But I think it would be much more graceful to inject some logic; e.g. if the clicked buttons group name is "Mens" make sure clear the state of any selected button in the "Womens" group. But I guess for me this is easier said than done.

If it does make more sense would I define the condition in my click function? (here is me hacking away at this logic - I realize my sytax is probably messed up)

Code JavaScript:
$(".cart input:radio").click(function(){
if(this.checked[name@Mens]){
$(radio[name@Womens]).checked = false;

[Code]....