Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

Photo
- - - - -

drinking in the bar


  • Please log in to reply
22 replies to this topic

#11 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1677 posts
  • Gender:Female

Posted 03 August 2013 - 02:52 PM

What would it take to contradict the axiom?
  • 0

#12 Rainman

Rainman

    Advanced Member

  • Members
  • PipPipPip
  • 143 posts

Posted 03 August 2013 - 04:13 PM

Spoiler for

  • 0

#13 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1677 posts
  • Gender:Female

Posted 03 August 2013 - 07:22 PM

Spoiler for actually

  • 0

#14 Rainman

Rainman

    Advanced Member

  • Members
  • PipPipPip
  • 143 posts

Posted 03 August 2013 - 08:17 PM

Spoiler for


  • 0

#15 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1677 posts
  • Gender:Female

Posted 03 August 2013 - 08:24 PM

Think about which in the P&Q (if p then q) is false with the second scenario.
  • 0

#16 Rainman

Rainman

    Advanced Member

  • Members
  • PipPipPip
  • 143 posts

Posted 03 August 2013 - 08:46 PM

P (someone is drinking) is true. Q (everyone is drinking) is false. So "if P then Q" is false.


  • 0

#17 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1677 posts
  • Gender:Female

Posted 03 August 2013 - 09:40 PM

So if someone is not drinking then p is false, so...
  • 0

#18 Rainman

Rainman

    Advanced Member

  • Members
  • PipPipPip
  • 143 posts

Posted 03 August 2013 - 10:01 PM

I see what you mean now, but no. The negation of P is "no one is drinking", not "someone is not drinking".
Someone is drinking = at least one person is drinking.
Someone is not drinking = at least one person is not drinking.
These statements are not mutually exclusive. If you are drinking and I am not drinking, then both are true.
  • 0

#19 BMAD

BMAD

    Senior Member

  • Members
  • PipPipPipPip
  • 1677 posts
  • Gender:Female

Posted 03 August 2013 - 10:44 PM

From wikipedia

Suppose that at least one person is not drinking. For any particular nondrinking person, it still cannot be wrong to say that if that particular person is drinking, then everyone in the pub is drinking because that person is, in fact, not drinking. In this case the condition is false, so the statement is vacuously true due to the nature of material implication in formal logic, which states that "If P, then Q" is always true if P (the condition or antecedent) is false. [1][2] Either way, there is someone in the pub such that, if he is drinking, everyone in the pub is drinking. A slightly more formal way of expressing the above is to say that if everybody drinks then anyone can be the witness for the validity of the theorem. And if someone doesn't drink, then that particular non-drinking individual can be the witness to the theorem's validity. [3] The proof above is essentially model-theoretic (can be formalized as such).

http://en.m.wikipedi...Drinker_paradox

Edited by BMAD, 03 August 2013 - 10:44 PM.

  • 0

#20 Rainman

Rainman

    Advanced Member

  • Members
  • PipPipPip
  • 143 posts

Posted 04 August 2013 - 08:13 AM

That's not the same statement. "There is someone in the pub, such that if he is drinking, everyone is drinking" is not the same as "if someone in the pub is drinking, then everyone is drinking". The first statement checks each person individually for the "if-then" statement, and asserts that at least one of those is true. The second statement is just another way of saying "no one is drinking or everyone is drinking", which is often false.

 

To illustrate the difference, suppose persons A and B are in the bar. A is drinking, B is not drinking. So someone in the bar is drinking. But everyone is not drinking.

The statement in the OP, "if someone is drinking, then everyone is drinking", is false (P is true, Q is false).

The statement on wikipedia, "there is someone in the pub, such that if he is drinking, then everyone is drinking", is in fact true. Let us check these two statements:

  • If A is drinking, then everyone is drinking. A is drinking, but everyone is not drinking. So this one is false.

  • If B is drinking, then everyone is drinking. Since B is not drinking, this statement is true by default.

So there is indeed such a person in the pub that the conditional statement is true, and that person is B. Hence there is someone in the pub, such that if he is drinking, then everyone is drinking.

 

In the OP, the man said something to the effect of "I noticed the first man was drinking, and if he is drinking then everyone is drinking". This is false unless everyone is in fact drinking. But, if he had seen someone who was not drinking, he could have safely pointed to the non-drinker and said "if that man is drinking, then everyone is drinking". That statement is true because the "if" part is false.


  • 0




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users