There are 4 shut doors in front of you. you know that each door has an animal painted on one side and a plant painted on the other side. the four doors have the following painted on the sides that you can see (one per door): a lily, a pine tree, a fox, and an eagle. you have been told that these doors satisfy the rule "if a door has a flower on its plant side, then it has a bird on its animal side". which is the smallest set of doors that you must check the hidden side of to determine conclusively whether this rule is true or false for these doors?