In a room there are only two types of people, namely Type 1 and Type 2. Type 1…
2015
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?
- A.
The result is head
- B.
The result is tail
- C.
If the person is of Type 2, then the result is tail
- D.
If the person is of Type 1, then the result is tail
Attempted by 94 students.
Show answer & explanation
Correct answer: A
Answer: The result is head.
Reason:
Let H mean the coin landed head, and let T mean the speaker tells the truth (T is true for Type 1, false for Type 2). The speaker says: “H if and only if T.”
Case 1 — speaker tells the truth (T is true): The spoken biconditional is true, so H iff true, which forces H to be true. Thus the coin is head.
Case 2 — speaker lies (T is false): The spoken biconditional is false. The content “H iff false” is equivalent to “not H.” For the liar the uttered statement must be false, so “not H” is false, which forces H to be true. Thus the coin is head.
In both possible cases the coin result is head, so the correct conclusion is that the result is head.
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