Case 1: Person is of type 1. Then he must be telling the truth. If so,the result of toss must be head. Case 2: Person is of type 2. Then he must be lying. The lie is "if I tell truth result is head' so the truth will be "if i tell truth result will be tail". But because he lies,he didn't tell truth and that's why result is head. Since result is head in all possible cases, option A is correct.
*I Think this would be an answer* "The result of the toss is head if and only if I am saying the truth." This statement can be written in logical terms as: Result is Head ↔ Person is telling the truth Result is Head↔Person is telling the truth This is a biconditional statement, meaning both sides of the statement must be true or both must be false for the statement to hold. Analysis: Let's consider both cases where the person can be either Type 1 (truth-teller) or Type 2 (liar). Case 1: The person is Type 1 (truth-teller) If the person is Type 1, they always tell the truth. According to the statement, if the person is telling the truth, then the result of the toss is head. Since the person is indeed telling the truth (being Type 1), the result must be head. Case 2: The person is Type 2 (liar) If the person is Type 2, they always lie. According to the statement, if the person is lying, then the result of the toss is not head (i.e., the result is tail). Since the person is lying (being Type 2), and the statement "The result is head if and only if I am saying the truth" is false, the result must be tail. Conclusion: From the analysis, we see: If the person is Type 1 (truth-teller), the result is head. If the person is Type 2 (liar), the result is tail. Now, let's match these conclusions with the options given: (a) The result is head. This is true if the person is Type 1, but not necessarily true if the person is Type 2. (b) The result is tail. This is true if the person is Type 2, but not necessarily true if the person is Type 1. (c) If the person is of Type 2, then the result is tail. This is always true based on our analysis. (d) If the person is of Type 1, then the result is tail. This is false based on our analysis, since if the person is Type 1, the result is head. The correct option is: (c) If the person is of Type 2, then the result is tail.
I propose a doubt here: at 3:06 you said "q=F means I am lying so it is not possible for type 1" but the point is type 1 did not give the statement "q", he only gave the statement "p if and only if q", so option c should be the answer. Is this right?
I think he made a mistake, he should have tossed out the above case because it contradicts the statement, so both case in type 2 is wrong. even then we get the answer heads only
Because of him belonging to Type 2, the 2nd part of his statement "iff I'm saying the truth" is a lie. Hence the 1st part "the result of the toss is head" is still a lie as it is implied upon the 2nd statement and conversely.
I think the video answer is correct, type 2 person is ¬q so it means "I'm laying" and "the result of toss coin is head" needs to be false, so it becomes p = F which is the same as "the result of toss coin is tail" or "the result of toss coin is not head" which is ¬p. and we know that ¬p ¬q = T. Lets remember that in biconditional statement only equal truth values gives T results. We know that this person told us a lie, and, if he is saying "the result of toss coin is not head" or "the result of toss coin is tail" so the answer is T, meaning that the real result is head, as the same as in the type one person.(this is only an opinion, if I'm wrong is cool, tell me, I'm learning too). new edit. lets take ¬p ¬q and turn it into two conditional statements ¬p => ¬q that would say "if The result of the toss coin is not heads" then "I´m lying" and ¬q => ¬p that would say "if I´m lying" then "The result of the toss coin is not heads". now, we know that everything that type person 2 says is lie, so ¬p turns into ¬(¬p) for this two conditional statements, and the final answer is heads. you can check the truth values to see the answer is truth and the logical equivalence between this biconditional and conditional statements.
So to answer your question, we forgot the second part of the statement, " Result of toss is head " which is "result of toss is head and I am not telling truth", once you take part of the statement out of context the meaning changes
Amazing question and awesome explanation 😃👍
Case 1: Person is of type 1. Then he must be telling the truth. If so,the result of toss must be head.
Case 2: Person is of type 2.
Then he must be lying. The lie is "if I tell truth result is head' so the truth will be "if i tell truth result will be tail". But because he lies,he didn't tell truth and that's why result is head.
Since result is head in all possible cases, option A is correct.
*I Think this would be an answer*
"The result of the toss is head if and only if I am saying the truth."
This statement can be written in logical terms as:
Result is Head
↔
Person is telling the truth
Result is Head↔Person is telling the truth
This is a biconditional statement, meaning both sides of the statement must be true or both must be false for the statement to hold.
Analysis:
Let's consider both cases where the person can be either Type 1 (truth-teller) or Type 2 (liar).
Case 1: The person is Type 1 (truth-teller)
If the person is Type 1, they always tell the truth.
According to the statement, if the person is telling the truth, then the result of the toss is head.
Since the person is indeed telling the truth (being Type 1), the result must be head.
Case 2: The person is Type 2 (liar)
If the person is Type 2, they always lie.
According to the statement, if the person is lying, then the result of the toss is not head (i.e., the result is tail).
Since the person is lying (being Type 2), and the statement "The result is head if and only if I am saying the truth" is false, the result must be tail.
Conclusion:
From the analysis, we see:
If the person is Type 1 (truth-teller), the result is head.
If the person is Type 2 (liar), the result is tail.
Now, let's match these conclusions with the options given:
(a) The result is head.
This is true if the person is Type 1, but not necessarily true if the person is Type 2.
(b) The result is tail.
This is true if the person is Type 2, but not necessarily true if the person is Type 1.
(c) If the person is of Type 2, then the result is tail.
This is always true based on our analysis.
(d) If the person is of Type 1, then the result is tail.
This is false based on our analysis, since if the person is Type 1, the result is head.
The correct option is:
(c) If the person is of Type 2, then the result is tail.
ıt was great Q and great explanation. My mind is so happy.
very good explanation
I thought it was a tail the answer (b), as a result of not considering the two cases.
Amazing tutorial.
I propose a doubt here:
at 3:06 you said "q=F means I am lying so it is not possible for type 1" but the point is type 1 did not give the statement "q", he only gave the statement "p if and only if q", so option c should be the answer.
Is this right?
I also think it should be c
please make the video on the three person knews knight spy
I don't get how the result is head fromq the equivalencies shown near the 4 minute mark
Why the result cant be option C ?
because if you want result = tail then T2 has to be true which can not happen.
If "Type 2" person always lie then it's statement " Result of toss is head " also become a lie.
Can anyone explain??
I think he made a mistake, he should have tossed out the above case because it contradicts the statement, so both case in type 2 is wrong. even then we get the answer heads only
Because of him belonging to Type 2, the 2nd part of his statement "iff I'm saying the truth" is a lie. Hence the 1st part "the result of the toss is head" is still a lie as it is implied upon the 2nd statement and conversely.
I think the video answer is correct, type 2 person is ¬q so it means "I'm laying" and "the result of toss coin is head" needs to be false, so it becomes p = F which is the same as "the result of toss coin is tail" or "the result of toss coin is not head" which is ¬p. and we know that ¬p ¬q = T. Lets remember that in biconditional statement only equal truth values gives T results. We know that this person told us a lie, and, if he is saying "the result of toss coin is not head" or "the result of toss coin is tail" so the answer is T, meaning that the real result is head, as the same as in the type one person.(this is only an opinion, if I'm wrong is cool, tell me, I'm learning too).
new edit.
lets take ¬p ¬q and turn it into two conditional statements ¬p => ¬q that would say "if The result of the toss coin is not heads" then "I´m lying" and ¬q => ¬p that would say "if I´m lying" then "The result of the toss coin is not heads". now, we know that everything that type person 2 says is lie, so ¬p turns into ¬(¬p) for this two conditional statements, and the final answer is heads. you can check the truth values to see the answer is truth and the logical equivalence between this biconditional and conditional statements.
So to answer your question, we forgot the second part of the statement, " Result of toss is head " which is "result of toss is head and I am not telling truth", once you take part of the statement out of context the meaning changes
my ex is type 2
just like you