Simplest solution. For both Radio and Checkboxes.
$('body').on('click', 'input[type="checkbox"]', function(){
if ($(this).attr('checked')){
$( this ).attr( 'checked', false);
} else {
$( this ).attr( 'checked', true);
}
});
$('body').on('click', 'input[type="radio"]', function(){
var name = $(this).attr('name');
$("input[name="+name+"]:radio").attr('checked', false);
$( this ).attr( 'checked', true);
});