Date Range Calculation .Any Suggestions?

I need to calculate some Date Ranges.

I have three Date Ranges:

1. 25 July 11 - 10 Oct 11
2. 05 Aug 11 - 05 Oct 11

3. 20 Aug 11 - 08 Nov 11

   I need to create a new membership for all the valid periods that can be before and after

   What is a good way to do this?

   Code Example

          public enum MembershipType
          {
             Gym=1,
             Magazine=2,
             Hotel=3
          }
          class Program
          {
             static void Main()
             {
                // During  1st Aug 2011 and 20th Oct 2011 Membership payment must be stopped
                var stopPaymentStartDate  =  new DateTime(2011,08,1);
                var stopPaymentEndDate    =  new DateTime(2011,10,20);
   
   
                var gymMembership = new Membership{MembershipType=MembershipType.Gym, StartDate = new DateTime(2011, 07, 25), EndDate = new DateTime(2011, 10, 10)};
                var magazineMembership = new Membership{MembershipType = MembershipType.Magazine,StartDate = new DateTime(2011, 08, 5),EndDate = new DateTime(2011, 10, 5)};
                var hotelMembership = new Membership{MembershipType = MembershipType.Hotel,StartDate = new DateTime(2011, 08, 20),EndDate = new DateTime(2011, 11, 8)};
   
                //How Can I get the wanted result below:
                //???
   
                //Wanted List of result as follows:
                var gymMembershipResult = new Result{MembershipType = MembershipType.Gym,StartDate = new DateTime(2011, 10, 10),EndDate = new DateTime(2011, 10, 20)};
                var magazineMembershipResultOne = new Result { MembershipType = MembershipType.Magazine, StartDate = new DateTime(2011, 08, 01), EndDate = new DateTime(2011, 08,05) };
                var magazineMembershipResultTwo = new Result { MembershipType = MembershipType.Magazine, StartDate = new DateTime(2011, 10, 05), EndDate = new DateTime(2011, 10, 20) };
                var hotelMembershipResult = new Result { MembershipType = MembershipType.Hotel, StartDate = new DateTime(2011, 08, 01), EndDate = new DateTime(2011, 08, 20) };
   
             }
          }
          public class Result
          {
             public DateTime StartDate { get; set; }
             public DateTime EndDate { get; set; }
             public MembershipType MembershipType { get; set; }
          }
          public class Membership
          {
             public DateTime StartDate { get; set; }
             public DateTime EndDate { get; set; }
             public MembershipType MembershipType { get; set; }
          }
       }
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class Program
{
    static void Main(string[] args)
    {
        DateTime stopPaymentStartDate = new DateTime(2011, 08, 1);
        DateTime stopPaymentEndDate = new DateTime(2011, 10, 20);

        MembershipPeriod gymMembership = new MembershipPeriod 
        { 
            MembershipType = MembershipType.Gym, 
            StartDate = new DateTime(2011, 07, 25), 
            EndDate = new DateTime(2011, 10, 10) 
        };

        MembershipPeriod magazineMembership = new MembershipPeriod 
        { 
            MembershipType = MembershipType.Magazine, 
            StartDate = new DateTime(2011, 08, 5), 
            EndDate = new DateTime(2011, 10, 5) 
        };

        MembershipPeriod hotelMembership = new MembershipPeriod
        { 
            MembershipType = MembershipType.Hotel, 
            StartDate = new DateTime(2011, 08, 20), 
            EndDate = new DateTime(2011, 11, 8) 
        };

        List<MembershipPeriod> resultsGym = GetResultsForPeriod(gymMembership, stopPaymentStartDate, stopPaymentEndDate);
        List<MembershipPeriod> resultsmagazine = GetResultsForPeriod(magazineMembership, stopPaymentStartDate, stopPaymentEndDate);
        List<MembershipPeriod> resultshotel = GetResultsForPeriod(hotelMembership, stopPaymentStartDate, stopPaymentEndDate);
    }

    private static List<MembershipPeriod> GetResultsForPeriod(MembershipPeriod period, DateTime stopPaymentStartDate, DateTime stopPaymentEndDate)
    {
        List<DateTime> datesToKeep = new List<DateTime>();

        for (DateTime date = stopPaymentStartDate.Date; date <= stopPaymentEndDate.Date; date = date.AddDays(1))
        {
            if (date <= period.StartDate.Date || date >= period.EndDate.Date)
            {
                datesToKeep.Add(date);
            }
        }

        List<MembershipPeriod> results = new List<MembershipPeriod>();
        MembershipPeriod newPeriod = null;

        for (int i = 0; i < datesToKeep.Count; i++)
        {
            if (newPeriod == null)
            {
                newPeriod = new MembershipPeriod();
                newPeriod.MembershipType = period.MembershipType;
                newPeriod.StartDate = datesToKeep[i];
            }

            if (i == datesToKeep.Count - 1 || (datesToKeep[i + 1] - datesToKeep[i]).Days > 1)
            {
                newPeriod.EndDate = datesToKeep[i];
                results.Add(newPeriod);
                newPeriod = null;
            }
        }

        return results;
    }
}

public enum MembershipType 
{ 
    Gym = 1, 
    Magazine = 2, 
    Hotel = 3 
}

public class MembershipPeriod 
{ 
    public DateTime StartDate 
    { 
        get; 
        set; 
    } 

    public DateTime EndDate 
    { 
        get; 
        set; 
    } 

    public MembershipType MembershipType 
    { 
        get; 
        set; 
    } 
}