I have the following in the page
You may use:
if ( frm.product.value=="F" ){
var $select_box = $('[name=val]');
$select_box.find('[value=A],[value=C]').remove();
}
Update: If you modify your select box a bit to this
the non-jQuery solution would be this
if ( frm.product.value=="F" ){
var elem = document.getElementById('A');
elem.parentNode.removeChild(elem);
var elem = document.getElementById('C');
elem.parentNode.removeChild(elem);
}