GATE CS 2015 Set 3 — Question 26
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Engineering Mathematics → Mathematical Logic → Propositional Logic
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Question
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?
Correct answer
(A) The result is head
Solution
Let be the proposition "The result is head" and be the proposition "The person is telling the truth".
The statement given by the person is .Case 1: The person is Type 1 (Truth-teller).
Then is true. Since they tell the truth, the statement must be true.
So, is true, which implies is true.Case 2: The person is Type 2 (Liar).
Then is false. Since they lie, the statement must be false.
So, is false. The biconditional is false if and only if and have different truth values.
Since is false, must be true for the statement to be false.In both cases, is true. Therefore, the result is head.
The statement given by the person is .Case 1: The person is Type 1 (Truth-teller).
Then is true. Since they tell the truth, the statement must be true.
So, is true, which implies is true.Case 2: The person is Type 2 (Liar).
Then is false. Since they lie, the statement must be false.
So, is false. The biconditional is false if and only if and have different truth values.
Since is false, must be true for the statement to be false.In both cases, is true. Therefore, the result is head.
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