Why aren't my functions being defined in the code.

//Problem:Hints are shown even when form is valid
//Solution: Hide and show them at appropriate times
var $password = $("#password");
var $confirmPassword = $("#confirm_password");

//Hide hints
$("form span").hide();

function isPasswordValid() {
  return $password.val().length > 8;
}

function arePasswordsMatching() {
  return $password.val() === $confirmPassword.val();
}

function canSubmit() {
  return isPasswordValid() && arePasswordsMatching();

function passwordEvent() {
   if(isPasswordValid()) {
    //Hide hints if valid
    $password.next().hide();
  } else {
    $password.next().show();
  //Else show hint
  }
}

function confirmPasswordEvent() {
  if(arePasswordsMatching()) {
    $confirmPassword.next().hide();
  } else {
    $confirmPassword.next().show();
  }
}

function enableSubmitEvent() {
   $("#submit").prop("disabled", !canSubmit());
 }
//When event happens on password input
$password.focus(passwordEvent).keyup(passwordEvent).keyup(confirmPasswordEvent).keyup(enableSubmitEvent); 

$confirmPassword.focus(confirmPasswordEvent).keyup(confirmPasswordEvent).keyup(enableSubmitEvent);
  //Find out if password is valid
//When event happen on confirmation input
  //Find out if password and confirmation match
  //Hind hints if matched
  //else show the hint
  enableSubmitEvent();