TYPE 1.T2: Teller is type 2.P = “Result is head if and only if I am in type 1”P = HʘT1CASE 1: P = FALSE (i.e Teller is type 2)\(\begin{array}{L}\bar H.\overline {T1} + H.T1 = FALSE\\T.T2 + H.T1 = FALSE\\T.T2 + H.T1 = FALSE\end{array}\) T = FALSE\(\therefore \bar T = TRUE\), THUS result is Head.CASE 2: P = TRUE (i.e. teller is type 1)\(\begin{array}{l}\bar H.\overline {T1} + H.T1 = TRUE\\T.T2 + HT1 = TRUE\\T.O + H = TRUE\end{array}\) ∴ H = TRUEHence OUTPUT is Head in both cases.

"> TYPE 1.T2: Teller is type 2.P = “Result is head if and only if I am in type 1”P = HʘT1CASE 1: P = FALSE (i.e Teller is type 2)\(\begin{array}{L}\bar H.\overline {T1} + H.T1 = FALSE\\T.T2 + H.T1 = FALSE\\T.T2 + H.T1 = FALSE\end{array}\) T = FALSE\(\therefore \bar T = TRUE\), THUS result is Head.CASE 2: P = TRUE (i.e. teller is type 1)\(\begin{array}{l}\bar H.\overline {T1} + H.T1 = TRUE\\T.T2 + HT1 = TRUE\\T.O + H = TRUE\end{array}\) ∴ H = TRUEHence OUTPUT is Head in both cases.

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In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell the truth and Type 2 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you till you ask for it. Upon asking, the person replies the following.“The result of the toss is head if and only if I am telling the truth.”Which of the following options is correct?

Logical and Verbal Reasoning Logic in Logical and Verbal Reasoning 1 year ago

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H: Result is head.T: Result is tail.T1: Teller is TYPE 1.T2: Teller is type 2.P = “Result is head if and only if I am in type 1”P = HʘT1CASE 1: P = FALSE (i.e Teller is type 2)\(\begin{array}{L}\bar H.\overline {T1} + H.T1 = FALSE\\T.T2 + H.T1 = FALSE\\T.T2 + H.T1 = FALSE\end{array}\) T = FALSE\(\therefore \bar T = TRUE\), THUS result is Head.CASE 2: P = TRUE (i.e. teller is type 1)\(\begin{array}{l}\bar H.\overline {T1} + H.T1 = TRUE\\T.T2 + HT1 = TRUE\\T.O + H = TRUE\end{array}\) ∴ H = TRUEHence OUTPUT is Head in both cases.

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