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The Exclusive Club (Posted on 2013-07-01) Difficulty: 3 of 5
There is a club called the Exclusive Club. Somebody is a member of this club if and only if he has not shaved anybody who has shaved him. In other words, X is a member of the Exclusive Club if and only if there is no Y such that X shaves Y and Y shaves X.

A barber once claimed that he had shaved every member of the Exclusive Club and nobody else. Show that the barber's claim cannot be true.

No Solution Yet Submitted by Math Man    
Rating: 5.0000 (1 votes)

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Some Thoughts re(3): solution | Comment 5 of 8 |
(In reply to re(2): solution by Steve Herman)

...everybody that is human is a member of the human race,,,

this is a tautology.

,,,,The problem is quite clear that somebody is a member of this club if he has not shaved anybody who has shaved him..., 

but the problem  does not say that everybody that has not shaved anybody who has shaved him  must  belong to this "exclusive " club.

1.You are free to join TEDC (Tzidon's  exclusive driving club )
IF AND ONLY IF you are holding a valid driving licence.
2. The management reserves the right of not admitting you without any explanation.

Ergo, one is free to join IF AND ONLY IF he  meets  the requirements.
He is also free not to join.

Is  it clear that the sentence as written (if and only if) specifies
the requirements, necessary but not sufficient,

There are 4 conditions to be the President of USA:

1. American citizenship
2. Born in the USA
3. Over  38 yrs of age

...oops   ... 4.  you must be elected as well. 

Edited on July 2, 2013, 12:52 am
  Posted by Ady TZIDON on 2013-07-02 00:45:30

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