Question

Problem 2 (18 pts) The lady or the tiger? There are two rooms. Each of them is occupied by either a tiger or a lady, but not both. There is also a sign on the door of each room. For Room I, if a lady is it, then the sign on the door is true, but if a tiger is in it, the sign is false. In Room II, the situation is the opposite: a lady in the room means the sign on the door is false, and a tiger in the room means the sign is true. Here are the signs: Room I At least one room contains a lady Room II The other room contains a lady Solve this problem in propositional logic: write down the given facts as sentences, convert them to clauses and then prove by refutation using resolution that a lady is in room 1

Answer 1

Solution:

Since it is mentioned in the problem statement that in every room there must be a tiger or a lady which means that if there is a tiger in a room then this implies that there is a lady in the other room. Thus, assuming the second statement is false implies that the first statement is true and (since we know that either both are true or both are false) we can conclude that both must be true.

Now let's have a look at the all the combinations in which way the lady and the tiger can be placed in Room 1 and Room 2

and those cases are:

Room 1	Room 2	Sign 1	Sign 2
Lady	Lady	True	False
Lady	Tiger	True	False
Tiger	Lady	True	True
Tiger	Tiger	False	True

As can be seen, only the case of Tiger in Room 1, Lady in Room 2 makes the statements both true, and no combination makes them both false.

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