couldn't e be false as well

So while I understand that A is false but could E be false as well. So with the afternoon shift there is only 3 available slots open but in the rules there are already 3 numbers to fill those slot and they have to be in the afternoon. So when 6th is on a Friday afternoon none of the other 3 numbers that can be placed in the afternoon can be placed because it takes up one of the spots.