level 7
我想说的是我是高手
2012年05月18日 21点05分
![[打酱油]](/static/emoticons/u6253u9171u6cb9.png)
level 6
level 6
Suppose three guys A,B,C.
Turn to A and ask
Question 1: Does da mean yes iff(*), you are True iff B is Random?
If A is True or False and you get the answer da, then as we have seen, B is Ra
ndom, and therefore C is either True or False; but if A is True or False and y
ou get the answer ja, then B is not Random, therefore B is either True or Fals
e.
But what if A is Random? If A is Random, then neither B nor C is Random! So if
A is Random and you get the answer da, C is not Random (neither is B, but tha
t’s irrelevant), and therefore C is either True or False; and if A is Random
and you get the answer ja, B is not random (neither is C, irrelevantly), and t
herefore B is either True or False.
Thus, no matter whether A is True, False, or Random, if you get the answer da
to Question 1, C is either True or False, and if you get the answer ja, B is e
ither True or False!
Now turn to whichever of B and C you have just discovered is either True or Fa
lse — let us suppose that it is B (if it is C, just interchange the names B a
nd C in what follows) — and ask:
Question 2: Does da mean yes?
True will answer da, and False will answer ja. Thus, with two questions, you h
ave either identified B as True or identified B as False.
For our third and last question, turn again to B, whom you have now either ide
ntified as True or identified as False, and ask:
Question 3: Does da mean yes iff A is Random?
Suppose B is True. Then if you get the answer da, then A is Random, and theref
ore A is Random, B is True, C is False, and you are done; but if you get the a
nswer ja, then A is not Random, so A is False, B is true, C is Random, and you
are again done.
Suppose B is False. Then if you get the answer da, then since B speaks falsely
, A is not Random, and therefore A is True, B is False, C is Random, and you a
re done; but if we get ja, then A is Random, and thus B is False, and C is Tru
e, and you are again done.
(*) iff = if and only if, biconditional, logic table as below:
T iff T = T
T iff F = F
F iff T = F
F iff F = T
2012年05月18日 21点05分
12
Turn to A and ask
Question 1: Does da mean yes iff(*), you are True iff B is Random?
If A is True or False and you get the answer da, then as we have seen, B is Ra
ndom, and therefore C is either True or False; but if A is True or False and y
ou get the answer ja, then B is not Random, therefore B is either True or Fals
e.
But what if A is Random? If A is Random, then neither B nor C is Random! So if
A is Random and you get the answer da, C is not Random (neither is B, but tha
t’s irrelevant), and therefore C is either True or False; and if A is Random
and you get the answer ja, B is not random (neither is C, irrelevantly), and t
herefore B is either True or False.
Thus, no matter whether A is True, False, or Random, if you get the answer da
to Question 1, C is either True or False, and if you get the answer ja, B is e
ither True or False!
Now turn to whichever of B and C you have just discovered is either True or Fa
lse — let us suppose that it is B (if it is C, just interchange the names B a
nd C in what follows) — and ask:
Question 2: Does da mean yes?
True will answer da, and False will answer ja. Thus, with two questions, you h
ave either identified B as True or identified B as False.
For our third and last question, turn again to B, whom you have now either ide
ntified as True or identified as False, and ask:
Question 3: Does da mean yes iff A is Random?
Suppose B is True. Then if you get the answer da, then A is Random, and theref
ore A is Random, B is True, C is False, and you are done; but if you get the a
nswer ja, then A is not Random, so A is False, B is true, C is Random, and you
are again done.
Suppose B is False. Then if you get the answer da, then since B speaks falsely
, A is not Random, and therefore A is True, B is False, C is Random, and you a
re done; but if we get ja, then A is Random, and thus B is False, and C is Tru
e, and you are again done.
(*) iff = if and only if, biconditional, logic table as below:
T iff T = T
T iff F = F
F iff T = F
F iff F = T
