Results 1 to 12 of 12

Math Help - Logic Proofs

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    13

    Logic Proofs

    Hello,

    I'm not getting credit for this questions, but was told there would be one like it on the quiz so I'm trying to figure it out.

    Write a proof sequence for the following assertion.



    I know I am given several things I just not sure how to start a proof. We kind of just were thrown in this and never having experience with it is making it a confusing but like any math I know practice will make me better, but first I need to understand how this work. Not only are proofs something new I have to do but the logic is all new so that doesn't help. I'd appreciate any help that can be given. I know it's not your job to do my work so hints are acceptable help.

    Thanks.
    Last edited by Newskin01; February 10th 2011 at 03:42 PM. Reason: Fixed the post so it is right now. Sorry
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Those are unknown logical symbols, at least to me.
    Please tell us what each means.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2011
    Posts
    13
    = not
    --> is if then
    ^ = and
    => is equivalent

    I hope this helps. Thanks for looking.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by Newskin01 View Post
    = not
    --> is if then
    ^ = and
    => is equivalent
    Those symbols are completely standard.
    BUT they are not in your original posting.
    Please edit the post to rid it of any special fonts which do not display very well.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,663
    Thanks
    603
    Hello, Newskin01!

    Did you even look at what you posted?


    Write a proof sequence for the following assertion.

    . . \bigg[\sim(\sim\!p \to q) \vee  (\sim\!p \:\wedge \sim\!q)\bigg] \:\Longleftrightarrow\:(\sim\!p \:\wedge \sim\!q)

    Is this what you meant?

    It is a rather silly statement, isn't it?


    The first part is: . \sim(\sim\!p \to q) \;\;=\;\;\sim(p \vee q) \;\;=\;\;\sim\!p\:\wedge \sim\!q


    The statement becomes:
    . . \bigg[(\sim\!p \:\wedge \sim\!q) \vee (\sim\!p \,\wedge \sim\!q)\bigg] \;\Longleftrightarrow\; (\sim\!p \:\wedge \sim\!q)

    which simplifies to:
    . . . . . . . . . . . . . (\sim\!p \:\wedge \sim\!q) \;\Longleftrightarrow\;(\sim\!p \:\wedge \sim\!q)

    which is true, of course.

    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by Newskin01 View Post
    Hello,

    I'm not getting credit for this questions, but was told there would be one like it on the quiz so I'm trying to figure it out.

    Write a proof sequence for the following assertion.

    (p-->q) "or" (p^q) => p^q
    Is it just my browser, can anyone else actually read this positing?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jan 2011
    Posts
    13
    Oh it doesn't look that way on my screen weird. I can post a picture to help. Logic Proofs-proof.jpg
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by Newskin01 View Post
    Oh it doesn't look that way on my screen weird. I can post a picture to help. Click image for larger version. 

Name:	Proof.jpg 
Views:	48 
Size:	30.9 KB 
ID:	20742
    When posting do not use special fonts.
    Not all browsers are equal.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Jan 2011
    Posts
    13
    I'm sorry. Will not happen again.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I'm going to trot out emakarov's standard question here: what rules of inference are you using? Natural deduction/Fitch style? Copi's 19 Rules? Something else?
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Jan 2011
    Posts
    13
    I'm going to trot out emakarov's standard question here: what rules of inference are you using? Natural deduction/Fitch style? Copi's 19 Rules? Something else?
    Natural deduction, didn't realize there were so many. I'm just starting in on the topic.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  12. #12
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,506
    Thanks
    765
    Here is a derivation of \neg p\land\neg q from an open assumption \neg(\neg p\to q) in natural deduction. From here, it is easy to construct the required derivation using the disjunction elimination rule.



    I assume that \bot is a primitive symbol (for falsehood) and \neg p is a contraction for p\to\bot. If you have other conventions and rules for negation, feel free to describe them. The labels in implication introduction rules show the assumptions that are closed by these rules.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Logic proofs
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: March 21st 2011, 04:39 PM
  2. Symbolic Logic Proofs
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 13th 2009, 07:56 PM
  3. Help with a few propositional logic proofs
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: February 10th 2009, 06:27 PM
  4. Logic Proofs
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: October 21st 2008, 09:02 AM
  5. Logic & Propositions & Proofs
    Posted in the Discrete Math Forum
    Replies: 13
    Last Post: September 9th 2008, 09:45 AM

Search Tags


/mathhelpforum @mathhelpforum