GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 8

Answer 1

If $\mathrm{A}$ is a knight, then his statement that both of them are knights is true, and both will be telling the truth. But that is impossible, because $\text{B}$ is asserting otherwise (that $\text{A}$ is a knave). If $\text{A}$ is a knave, then $\text{B's}$ assertion is true, so he must be a knight, and $\text{A's}$ assertion is false, as it should be. Thus we conclude that $\text{A}$ is a knave and $\text{B}$ is a knight.

Comments

@Deepak Poonia @Sachin Mittal 1

Hi sir,

As per my understanding, I am getting 2 option:

1. here if A is saying truth, then both A and B are Knights. It means B is telling lie because he is saying “A is Knave” which is wrong. Then B is Kanve. Conclusion: A is Knight and B is Knave.
2. Another one, If B is telling truth that A is knave only. It means A is telling lie because both cannot be Knights. Then A is Knave. Conclusion: A is Knave and B is Knight.

Sir, can you please tell me where is my understanding wrong?

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@niloyy2012 in your option 1, you are assuming A is knight and saying truth i.e. “A and B are both knights” is true. And in the end you are concluding that B is knave ??? Isn't that a contradiction 

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@geekybread

Like in option 1: let’s say A is telling truth means A and B both are knights
Then as per the statement of B, that is wrong one it means B is telling lie. So B is knave.

Like this way, I am thinking. Please correct me if I am wrong.

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@niloyy2012 yes that's right but now think further, you have accepted that A and B are both knights so how are you getting B as knave and lying ? Both of these things cannot happen at the same time(B can’t be both knight and knave). This is a contradiction so this case can't be possible.

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@geekybread

Thanks bro. missed that.. 🙏

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Detailed Video Solution is here: Weekly Quiz 4 Solutions

Answer 2

Ans is C.

Comments

.

Answer 3

This puzzle type of questions can be easily solved by truth table and contradictions.

Assume 2 propositional variables P and Q where – 

P: “A is Knight”, ~ P: “A is Knave”

Q: “B is Knight”, ~ Q: “B is Knave”

Given information:

1. Knight always says truth means statement made by a Knight is always TRUE.
2. Knave always says false means statement made by a Knave is always FALSE.

Based on the information, there can be only 4 possibility with 2 persons A and B.

Statement made by A: “The two of us are both Knights” $\equiv P\wedge Q$

Statement made by B: “A is a Knave” $\equiv \sim P$

P (Type of A)	Q (Type of B)	Statement made by A	Statement made by B	Meaning
TRUE	TRUE	TRUE	FALSE	Assumption is B is Knight (Q = True) and Knight always says True but B (Knight) made a false statement which is a contradiction so this is not possible
TRUE	FALSE	FALSE	FALSE	Assumption is A is Knight (P = True) and Knight always says True but A (Knight) made a false statement which is a contradiction so this is not possible
FALSE	TRUE	FALSE	TRUE	Assumption is A is Knave (P = False) and Knave always says False and A (Knave) actually made a false statement which is consistent this is possible. Similarly we assumed B is Knight and B made a True statement so this is also consistent.
FALSE	FALSE	FALSE	TRUE	Assumption is B is Knave (Q = False) and Knave always says False but B (Knave) made a true statement which is a contradiction so this is not possible

 

Note that we got the contradictions in 3 cases as per the assumption so the assumption must be false in this 3 cases but 1 case is giving consistent results as per our assumption so this assumption must be true.

The answer would be Option C (A = Knave, B = Knight) corresponding to case 3 (P = False, Q = True).

Comments

Solving using Truth Table is a long process,

but it can easily create a mental model of how the concepts are being laid out. That is a very Good Explanation.

Answer 4

A says both A and b are knight

but b says A is knauve (knauve lie given in question)

hence A is knauve and B is knight