我可以同时使用快捷符号$和jQuery吗

我正在尝试在提交之前验证表单。验证工作正常，但表单未提交。我对jQuery没有足够的了解，但我怀疑这是因为同时使用快捷方式$和jQuery，我是对的还是问题出在其他地方？

代码：

<script type="text/javascript">
  $('p select[name=country]').change(function(){
  if ($('p select[name=country]').val() =='Au')
  {
  $('#seldivi').show();
  }
else
    {
    $('#seldivi').hide();
    }
});

        $(function(){
    $("a.mytrigger").click(function(e){
        var index = $(this).attr("href").substr(5);
        $('#navigation li:nth-child('+parseInt(index)+') a').click();
        e.preventDefault();
    });
});
//when i remove the following segment of codes the form submitted as usual but when  this portion exists the form is not submitted  
            jQuery(function(){
                jQuery("#ValidField").validate({
                    expression: "if (VAL) return true; else return false;",
                    message: "Please enter the Required field"
                });
                jQuery("#ValidNumber").validate({
                    expression: "if (!isNaN(VAL) && VAL) return true; else return false;",
                    message: "Please enter a valid number"
                });
                jQuery("#ValidInteger").validate({
                    expression: "if (VAL.match(/^[0-9]*$/) && VAL) return true; else return false;",
                    message: "Please enter a valid integer"
                });
                jQuery("#ValidDate").validate({
                    expression: "if (!isValidDate(parseInt(VAL.split('-')[2]), parseInt(VAL.split('-')[0]), parseInt(VAL.split('-')[1]))) return false; else return true;",
                    message: "Please enter a valid Date"
                });
                jQuery("#ValidEmail").validate({
                    expression: "if (VAL.match(/^[^''W][a-zA-Z0-9''_''-''.]+([a-zA-Z0-9''_''-''.]+)*''@[a-zA-Z0-9_]+(''.[a-zA-Z0-9_]+)*''.[a-zA-Z]{2,4}$/)) return true; else return false;",
                    message: "Please enter a valid Email ID"
                });
                jQuery("#ValidPassword").validate({
                    expression: "if (VAL.length > 5 && VAL) return true; else return false;",
                    message: "Please enter a valid Password"
                });
                jQuery("#ValidConfirmPassword").validate({
                    expression: "if ((VAL == jQuery('#ValidPassword').val()) && VAL) return true; else return false;",
                    message: "Confirm password field doesn't match the password field"
                });
                jQuery("#ValidSelection").validate({
                    expression: "if (VAL != '0') return true; else return false;",
                    message: "Please make a selection"
                });
                jQuery("#ValidMultiSelection").validate({
                    expression: "if (VAL) return true; else return false;",
                    message: "Please make a selection"
                });
                jQuery("#ValidRadio").validate({
                    expression: "if (isChecked(SelfID)) return true; else return false;",
                    message: "Please select a radio button"
                });
                jQuery("#ValidCheckbox").validate({
                    expression: "if (isChecked(SelfID)) return true; else return false;",
                    message: "Please check atleast one checkbox"
                });

   });
            /* ]]> */