HashSet таки добавляет дубликаты

public class People
    {
        public string name { get; set; }
        public int age { get; set; }
    }
 
    class Program
    {
        static void Main(string[] args)
        {
            HashSet<People> lydi = new HashSet<People>();
            lydi.Add(new People { name = "Vasya", age = 18 });
            lydi.Add(new People { name = "Vasya", age = 18 });
            lydi.Add(new People { name = "Vasya", age = 18 });
 
            Console.WriteLine("Count = " + lydi.Count); //выводит Count = 3 (((а надо 1
            Console.ReadKey();
        }
    }

struct Foo
{
   public int X { get; set; }
}
class Person : RealHashSet
{
   public string Name { get; set; }
   public Foo Bar { get; set; }
}
 
var a = new Person { Name = "A" };
var b = new Person { Name = "B" };
a.Equals(b); // KABOOM!

using System;
using System.Collections.Generic;
 
public class People
{
    public string name { get; set; }
    public int age { get; set; }
 
    public override bool Equals(object obj)
    {
        People q = (People)obj;
        return q != null && q.name == this.name && q.age == this.age;
    }
 
    public override int GetHashCode()
    {
        return this.name.GetHashCode() ^ this.age.GetHashCode();
    }
}
 
class Program
{
    static void Main(string[] args)
    {
        HashSet<People> lydi = new HashSet<People>();
        lydi.Add(new People { age = 18 });
 
        Console.WriteLine("Count = " + lydi.Count); //выводит Count = 3 (((а надо 1
        Console.ReadKey();
    }
}

public static class ComparerGenerator<T>
{
    private static readonly IEqualityComparer<T> EqualityComparerBackfield = CreateComparer();
 
    public static IEqualityComparer<T> EqualityComparer
    {
        get { return EqualityComparerBackfield; }
    }
 
    private static IEqualityComparer<T> CreateComparer()
    {
        throw new NotImplementedException();
    }
}