Discrete Structures plz write clear You stumble upon two trolls playing Stratego

Question

Discrete Structures

plz write clear

You stumble upon two trolls playing Stratego. They tell you: Troll 1: If we are cousins, then we are both knaves. Troll 2: We are cousins or we are both knaves. Could both trolls be knights? Recall that all trolls are either always-truth-telling knights or always-lying knaves. Holmes owns two suits: one black and one tweed. He always wears either a tweed suit or sandals. Whenever he wears his tweed suit and a purple shirt, he chooses to not wear a tie. He never wears the tweed suit unless he is also wearing either a purple shirt or sandals. Whenever he wears sandals, he also wears a purple shirt. Yesterday, Holmes wore a bow tie. What else did he wear?

Explanation / Answer

3.1 Propositional Logic

Given that both the trolls are either truth telling knights or always lying knaves.

We would have two cases:

case 1: Truth telling Knights.

Troll 1 : If we are cousins, then we both are knaves.

(for this to be possible they both should not be cousins).

Troll 2 : We are cousins, or we both are knaves.

(here for the troll 2 as we have assumed him to be truth telling Knight, and to valid troll 1 statement we have inferred that they both are not cousins. We can now say that Troll 2 cannot be a truth telling knight.)

Case 2 : Lying knaves

Troll 1 : If we are cousins, then we both are knaves.

(As we have assumed him to be always lying, we can confirm that whatever he says is always false (lie))

we can either say that- they are cousins, but are not knaves. Which is not possible. Because we have assumed them to be knaves. So that leaves with the possibility that, both are not cousins, but are knaves.

Troll 2 : We are cousins, or we both are knaves.

Assuming troll 2 be lying knaves, as inferring pon that they are not cousins. We cannot fully state the statement by Troll 2 be either true or false.

So finally we could say that the trolls cannot be knights.

Investigate

Holmes has 2 suits (black and tweed)

He always wear either of tweed suit or sandals i.e. he can wear tweed suit or sandals, or both on any given day.

IF he wants to wear a tie, he must not wear a tweed suit and purple shirt together.

He wears tweed suit if and only if he wears a purple shirt or sandals. But whenever he wears sandals he wears a purple shirt.

If he choses to wear sandals, he has to wear purple shirt. Now he can either wear tweed suit or a black suit. If he choses to wear a tweed suit he cannot wear a tie. And if choses to wear a black suit he can wear either a tie or a bow.

According to the problem statement, he wore a bow tie. so either he could have wore a set 1 : (sandals, purple shirt,tweed suit) or set 2 :(sandals, purple shirt, black suit)

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.