Options with a "yes" or "no" radio button
This should work:

$('#Option1, #Option2').live('change', function() {
    if ($('input[name=' + $(this).attr('id') + ']:checked').val() == 'False') {
        $('#formDiv').show();
    else {
        $('#formDiv').hide();
    }

    });


Or, if whatever has the id option1 is the same page element as the input with the name option1, you could do:

$('#Option1, #Option2').live('change', function() {
    if ($(this).val() == 'False')
        $('#formDiv').show();
    else {
        $('#formDiv').hide();
    }

    });