This is my solution:
public static bool OverlappingPeriods(DateTime aStart, DateTime aEnd,
DateTime bStart, DateTime bEnd)
{
if (aStart > aEnd)
throw new ArgumentException("A start can not be after its end.");
if(bStart > bEnd)
throw new ArgumentException("B start can not be after its end.");
return !((aEnd < bStart && aStart < bStart) ||
(bEnd < aStart && bStart < aStart));
}
I unit tested it with 100% coverage.