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Logic Warmups

Truth-tellers and Liars Warmup


Suppose you are visiting an island with knights, who always tell the truth, and knaves, who always lie.

You come across two islanders named Arnav and Bella.

Arnav says, "Bella is a knave."

Bella says, "Arnav is a knave."

How many of them are knights?

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 are these men? Both honest? Both liars? Or one of each, and, in that case, who is who?

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.)

\[ \text{This statement is false.} \]

Is the sentence above always a logical contradiction?


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