You have to write your own method in order to detect appointment conflicts (collisions). This method will have O(n²) complexity, where n specifies the number of appointments in your schedule. The following method, for example, detects whether there are any collisions in a specified schedule:

public bool DetectCollisions(Calendar calendar)
{
	foreach (Item i in calendar.Schedule.Items)
	{
		foreach (Item j in calendar.Schedule.Items)
		{
			if (j.StartTime <= i.StartTime && i.StartTime < j.EndTime ||
				j.StartTime < i.EndTime && i.EndTime <= j.EndTime)
				return true;
		}
	}

	return false;
} 

I haven't tested this one, so it might not work precisely as intended, but it can give you an idea.

Meppy