一个房间里只有两种人,即1型和2型。1型的人总是说真话,2型的人总是说谎。你给了那个房间里的一个人一枚公平的硬币,不知道他是哪种类型的人,并告诉他扔硬币并向你隐藏结果,直到你提出要求。经询问,此人回复如下:
“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)如果这个人是类型 2,那么结果是尾巴
(D)如果这个人是类型 1,那么结果是 tai答案:(一)
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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