You can do
$('.myCheckbox').attr('checked',true) //Standards compliant
or
$("form #mycheckbox").attr('checked', true)
If you have custom code in the onclick event for the checkbox that you want to fire, use this one instead:
$("#mycheckbox").click();
You can uncheck by removing the attribute entirely:
$('.myCheckbox').removeAttr('checked')
You can check all checkboxes like this:
$(".myCheckbox").each(function(){
$("#mycheckbox").click()
});