### Some Logic Problems

The following problems are adapted from a book of Logic Problems by
Raymond Smullyan: The Lady or the Tiger? and Other Logic Puzzles, Times
Books, 1982.
Last updated 02/02/97
Solution of these problems does involve applications of the rules of
propositional logic (plus some translations from words to symbols).
Enjoy!

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### Danger or Freedom

The first series of problems involve a mythical kingdom in which
prisoners are taken into a room and, after some hints, given a choice of
doors to open. Each door may lead to freedom or it may lead to
danger (a tiger who will kill them).
Each door has a sign on it with a sentence.
## Second Day

The king decided to make the puzzles more difficult. If the first door leads to freedom, then the sign on that door is true; if the first door leads to danger, then the sign on that door is false.

For the second door, this is reversed: if the second door leads to freedom, the sign on the second door is false; if the second door leads to danger, the sign on the second door is true.

### Fourth Problem

- The sign on the first door reads:

Both doors lead to freedom.
- The sign on the second door reads:

Both doors lead to freedom.

Now which door do you choose?
## First Day

### Third Problem

In the third trial, you are told that, again, either both signs are true or both signs are false. There are still two doors:
- The sign on the first door is:

Either this door leads to danger or the other door leads to
freedom.
- The sign on the second door is:

The other door leads to freedom.

### Second Problem

In the second trial, there are two doors:
- The sign on the first door is:

At least one of these doors leads to freedom.
- The sign on the second door is:

The other door leads to danger.

You are given one further ** hint **

Either both signs are true or both signs are false!
Which door should you choose?

### First Problem

In the first situation, there are two doors:
- The sign on the first door is:

This door leads to freedom and the other door leads to danger.
- The sign on the second door is:

One door leads to freedom and the other door leads to danger.

You are given one further ** hint **

One sign is true and the other is false!
Which door should you choose?

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