GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 15

Answer 1

$\text{Case 1:}$ Boy has black hair, Girl has white hair :
In this case, no one is lying, But we know at least one of them is lying, So, this case is not possible.

$\text{Case 2:}$ Boy has white hair, Girl has black hair :
Now, both are lying.

So, both are lying.

Detailed Video Solution: https://youtu.be/nclBhBmtz2g?t=2299

Answer 2

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

Since there are exactly 1 boy and 1 girl so the truth table will have only 2 cases (both being boy and both being girl would not be possible so these cases are not taken)

Statement made by black hair child: “I am a boy” so it will be true if he/she is a boy and false if he/she is a girl

Statement made by white hair child: “I am a girl” so it will be true if he/she is a girl and false if he/she is a boy

Gender of Black hair child	Gender of White hair child	Statement made by Black hair child	Statement made by White hair child	Meaning
Boy	Girl	TRUE	TRUE	Given that at least 1 of them is lying meaning as per the assumption of gender of black and white hair child, at least 1 of the statements must be FALSE but the statements made by both of them are true which implies it’s a contradiction and it cannot be possible.
Girl	Boy	FALSE	FALSE	Given that at least 1 of them is lying meaning as per the assumption of gender of black and white hair child, at least 1 of the statements must be FALSE and we notice that the statements made by both of them are false which is consistent with our assumption so this case is possible. Also note that both of the child are lying as both of their statements are FALSE.

 

Note that we got the contradictions in first case as per the assumption so the assumption must be false in this case but 2^nd case is giving consistent results as per our assumption so this assumption must be true.

The answer would be Option C (Both are lying) corresponding to case 2.

Answer 3

Assume the boy is lying (you can assume for girl as well) then he is saying "i am a girl" as the boy is a liar and won't confess that he is a boy , but the girl can say that she is a girl but the only other statement left is "i am a boy" and we know that ATLEAST one is lying therefore the girl is definitely lying(as she is saying "i am a boy"), so I can say that BOTH are lying.

Thanks for reading and pls correct me if i am wrong.

Answer 4

According to the question we have