📜  门| GATE-CS-2015(套装3)|第 65 题

📅  最后修改于: 2021-09-27 05:44:25             🧑  作者: Mango

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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