Results 1 to 8 of 8

Math Help - question on notion of 'proves'...

  1. #1
    NYC
    NYC is offline
    Newbie
    Joined
    Apr 2010
    Posts
    19

    question on notion of 'proves'...

    Is it possibe to have
    A proves B
    and
    not A proves B

    I'm tending towards thinking you can't, but not sure why. Any ideas?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member oldguynewstudent's Avatar
    Joined
    Oct 2009
    From
    St. Louis Area
    Posts
    241
    Quote Originally Posted by NYC View Post
    Is it possibe to have
    A proves B
    and
    not A proves B

    I'm tending towards thinking you can't, but not sure why. Any ideas?
    I'm not sure what you mean by "proves". If you mean implies then the answer is yes.

    p q p-->q

    T T T
    T F F
    F T T
    F F T
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2006
    Posts
    71
    Quote Originally Posted by NYC View Post
    Is it possibe to have
    A proves B
    and
    not A proves B

    I'm tending towards thinking you can't, but not sure why. Any ideas?
    No (at least as I read your question).

    But here's a valid sequent you might consider.

    A->B, ~A->B |- B or alternatively,

    |- (A->B) -> ((~A->B) -> B),

    or getting conjunction into the "equation",

    |- ((A->B) & (~A->B)) -> B
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,513
    Thanks
    769
    Is it possibe to have
    A proves B
    and
    not A proves B
    This is possible iff B is provable by itself.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    NYC
    NYC is offline
    Newbie
    Joined
    Apr 2010
    Posts
    19
    Quote Originally Posted by emakarov View Post
    This is possible iff B is provable by itself.
    Thanks
    In this case is B a tautology?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member oldguynewstudent's Avatar
    Joined
    Oct 2009
    From
    St. Louis Area
    Posts
    241
    Quote Originally Posted by NYC View Post
    Thanks
    In this case is B a tautology?
    You betcha!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    NYC
    NYC is offline
    Newbie
    Joined
    Apr 2010
    Posts
    19
    Quote Originally Posted by oldguynewstudent View Post
    You betcha!
    Thanks for the quick response!
    How would you show that B is a tautology?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member oldguynewstudent's Avatar
    Joined
    Oct 2009
    From
    St. Louis Area
    Posts
    241
    Quote Originally Posted by NYC View Post
    Thanks for the quick response!
    How would you show that B is a tautology?
    That would depend on B. Do you have the example of your actual problem?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Notion of Limits and Infinite Series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 22nd 2010, 05:50 PM
  2. Underlined letter in matrix notion
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: May 6th 2010, 03:47 PM
  3. Proves in Group Theory
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 4th 2010, 09:34 AM
  4. proves -discrete math !!! please help!!!
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 20th 2008, 07:40 PM
  5. induction,irrational and proves......
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: December 18th 2006, 10:30 AM

Search Tags


/mathhelpforum @mathhelpforum