Propositional Logic (Solved Problem 1)

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Discrete Mathematics: Propositional Logic (Solved Problem 1)
Topics discussed:
1. The solution of GATE-2015 question based on propositional logic.

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Axol x Alex Skrindo - You [NCS Release]

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Комментарии
Автор

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?

rajgopalpaithara
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Amazing question and awesome explanation 😃👍

shivamchauhan
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ıt was great Q and great explanation. My mind is so happy.

premuhendis
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please make the video on the three person knews knight spy

iftikhar
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I don't get how the result is head fromq the equivalencies shown near the 4 minute mark

timewrath
Автор

I thought it was a tail the answer (b), as a result of not considering the two cases.
Amazing tutorial.

Learn-With-Omar
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If "Type 2" person always lie then it's statement " Result of toss is head " also become a lie.

Can anyone explain??

kshitij
Автор

*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.

ashensamuditha