using System;

using System.Linq;

using System.Xml;

using System.Xml.Linq;

​

public class Program

{

    public static void Main(string[] args)

    {

        var doc = new XDocument(new XElement("parent", new XElement("child", 1)));

​

        var parent = doc.Descendants("parent").Single();

​

        var duplicateChild = new XElement("child", 1);

        var newChild = new XElement("child", 2);

​

        if (!parent.Elements().Any(e => XNode.DeepEquals(e, duplicateChild)))

        {

            parent.Add(duplicateChild);

        }

​

        if (!parent.Elements().Any(e => XNode.DeepEquals(e, newChild)))

        {

            parent.Add(newChild);            

        }

​

        Console.WriteLine(doc);

    }

}