How to create html element using JavaScript and create class/id to it

I want to create html element using JavaScript and add class or id, so I can edit this element later.

I know how to create element:

<html>

<body>
  <div id="new">
    <p id="p1">a</p>
    <p id="p2">b</p>
  </div>
  <script>
    var tag = document.createElement("p");
    var text = document.createTextNode("c");
    tag.appendChild(text);
    var element = document.getElementById("new");
    element.appendChild(tag);
  </script>
</body>

</html>

But I don’t know how to add class or id to element that don’t have id or class at beggining.