Results 1 to 3 of 3

Math Help - Liar Paradox

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    2

    Liar Paradox

    True, false, or other:

    If 1+1=3, then 1=0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303
    Truth table

    P Q P⇒Q
    T F F
    T T T
    F T T
    F F T

    So, P is false and Q is false in your case. Thus, the statement is true.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member Gamma's Avatar
    Joined
    Dec 2008
    From
    Iowa City, IA
    Posts
    517

    Vacuously True

    This statement is an example of something that is vacuously true. Since the hypothesis is always false and will never be met, you could put literally anything you want after the then and it would be true.

    If 1+1=3, then I am a purple cow. Sure this is true because 1+1 \not = 3.

    Another way to think about this would be to take the contrapositive of the statement and this is logically equivalent to the original statement and you see this is:
    If 1 \not = 0, then 1+1 \not = 3.

    The first is true and the second statement is true, so the statement is true. Notice because the second statement is always true it doesn't matter what the first statement is, so these two methods of analysis agree.
    Last edited by Gamma; April 22nd 2009 at 10:11 PM. Reason: typo
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A paradox
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: August 13th 2011, 04:08 PM
  2. Identify liar/truthful
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 7th 2009, 02:26 AM
  3. Paradox?
    Posted in the Geometry Forum
    Replies: 2
    Last Post: January 18th 2009, 01:03 PM
  4. Can someone help me with this paradox
    Posted in the Geometry Forum
    Replies: 2
    Last Post: October 18th 2008, 02:31 PM
  5. Liar/Truth Question
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: September 28th 2006, 06:52 PM

Search Tags


/mathhelpforum @mathhelpforum