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?
I think if you opened one door you could see the backside of all of the others to determine if this was true or not.
If a door has a flower on its plant side, then it has a bird on its animal side.
You have to open every door that has a flower on its plant side ---> so you have to open the door with a lily on it.
An equivalent logical statement is its contrapositive.
If a door does not have a bird on its animal side, the it does not have a flower on its plant side.
You have to open every door that does not have a bird on its animal side ---> so you have to dopen the door with a fox on it.
You have to open two doors.
You don't have to open the other two doors.