在一个房间中,只有两种类型的人,即类型1和类型2。类型1的人总是说实话,类型2的人总是在说谎。您给那个房间里的人一个公平的硬币,却不知道他来自哪一类型,并告诉他扔掉它并向您隐藏结果,直到您要它为止。在询问后,此人回复了以下内容:
“The result of the toss is head if and only if I am telling the truth.”
以下哪个选项是正确的?
(A)结果是头
(B)结果是尾巴
(C)如果该人属于2型,则结果为尾巴
(D)如果该人属于1型,则结果为tai答案: (A)
解释:
“The result of the toss is head if and only
if I am telling the truth.”
If the person is of Type 1 who always tell truth, then result must be head.
If the person is of Type 2 who always tell lie, then result must be head.
Negation of a sentence of the form "X is true if and only if Y is true" is
"Either X is true and Y is false, or X is false and Y is true."
Refer: http://math.stackexchange.com/questions/10435/negation-of-if-and-only-if
Which means "Either toss is head and I am not telling truth, or toss is tail
and I am telling truth".
Since the person always lie, it is "Either toss is head and I am not telling truth"
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