Can anyone simplify this Algorithm for me?

Question

Basically I just want to check if one time period overlaps with another. Null end date means till infinity. Can anyone shorten this for me as its quite hard to read at times. Cheers

    public class TimePeriod
    {
        public DateTime StartDate { get; set; }
        public DateTime? EndDate { get; set; }

        public bool Overlaps(TimePeriod other)
        {
            // Means it overlaps
            if (other.StartDate == this.StartDate
                || other.EndDate == this.StartDate
                || other.StartDate == this.EndDate
                || other.EndDate == this.EndDate)
                return true;

            if(this.StartDate > other.StartDate)
            {
                // Negative
                if (this.EndDate.HasValue)
                {
                    if (this.EndDate.Value < other.StartDate)
                        return true;
                    if (other.EndDate.HasValue && this.EndDate.Value < other.EndDate.Value)
                        return true;
                }

                // Negative
                if (other.EndDate.HasValue)
                {
                    if (other.EndDate.Value > this.StartDate)
                        return true;
                    if (this.EndDate.HasValue && other.EndDate.Value > this.EndDate.Value)
                        return true;
                }
                else
                    return true;
            }
            else if(this.StartDate < other.StartDate)
            {
                // Negative
                if (this.EndDate.HasValue)
                {
                    if (this.EndDate.Value > other.StartDate)
                        return true;
                    if (other.EndDate.HasValue && this.EndDate.Value > other.EndDate.Value)
                        return true;
                }
                else
                    return true;

                // Negative
                if (other.EndDate.HasValue)
                {
                    if (other.EndDate.Value < this.StartDate)
                        return true;
                    if (this.EndDate.HasValue && other.EndDate.Value < this.EndDate.Value)
                        return true;
                }
            }

            return false;
        }
    }

Answer 1

public bool Overlaps(TimePeriod other)
{
    return (other.StartDate >= StartDate && 
               (EndDate == null || other.StartDate <= EndDate.Value)) ||
           (StartDate >= other.StartDate &&
               (other.EndDate == null || StartDate <= other.EndDate.Value))
}

Answer 2

How about this one:

public bool Overlaps(TimePeriod other)
{
    bool isOtherEarlier = this.StartDate > other.StartDate;
    TimePeriod earlier = isOtherEarlier  ? other : this;
    TimePeriod later = isOtherEarlier ? this : other;
    return !earlier.EndDate.HasValue || earlier.EndDate > later.StartDate;
}