Override equals and operator equals on value types

Seems that if one defines a struct and if you encounter this rule, you will afterwards also encounter a compiler warning stating:

Warning 1 'xxx' overrides Object.Equals(object o) but does not override Object.GetHashCode
Warning 2 'xxx' defines operator == or operator != but does not override Object.GetHashCode

The following example shows a structure (value type) that violates this rule.

[C#]

using System;
namespace Samples
{
    // Violates this rule
    public struct Point
    {
        private readonly int _X;
        private readonly int _Y;

        public Point(int x, int y)
        {
            _X = x;
            _Y = y;
        }

        public int X
        {
            get { return _X; }
        }

        public int Y
        {
            get { return _Y; }
        }
   }
}

The following example fixes the above violation by overriding ValueType.Equals and implementing the equality operators (==, !=).

[C#]

using System;

namespace Samples
{
    public struct Point : IEquatable<Point>
    {

        private readonly int _X;
        private readonly int _Y;

        public Point(int x, int y)
        {
            _X = x;
            _Y = y;
        }

        public int X
        {
            get { return _X; }
        }

        public int Y
        {
            get { return _Y; }
        }

        public override int GetHashCode()
        {
            return _X ^ _Y;
        }

        public override bool Equals(object obj)
        {
            if (!(obj is Point))
                return false;

            return Equals((Point)obj);
        }

        public bool Equals(Point other)
        {
            if (_X != other._X)
                return false;

            return _Y == other._Y;
        }

        public static bool operator ==(Point point1, Point point2)
        {
            return point1.Equals(point2);
        }

        public static bool operator !=(Point point1, Point point2)
        {
            return !point1.Equals(point2);
        }
    }
}