Logic

Truth-tellers and Liars Warmup

In a mystical land where the animals talk, it is known that the rats always lie and the mice always tell the truth. If you ask a rat "Are you a rat?", what would it say?

Suppose I make the claim:

$\color{purple} { \text{If it's raining, I have my umbrella.} }$

If I am lying, which of these must be the case?

Honest men always tell the truth and liars always lie. What can be said about these men?

(Note that "one of two of us" is used in the sense of "only one of the two of us".)

You are in a dungeon and come across three doors; one contains a treasure, and the other two lead to bottomless pits.

The doors have signs. You know the door that leads to treasure has a sign that is false and the other signs are true.

Which door should you take to get the treasure? (Remember, the sign on the door that leads to treasure is false.)

Leonardo, Steve and Jerry are three woodland creatures. One of them is a lion that always tells the truth, one of them is a snake that always lies, and one of them is a jackal that either tells the truth or a lie. How many of them (without a prior question) can make the following statement?

"I am a snake."

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