Results 1 to 7 of 7

Math Help - Proposition Logic problem

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    15

    Proposition Logic problem

    Anyone good with proposition logics? that can help out?
    im stuck on one question and can't figure out the next step.

    The question states : Use the rules of inference to prove the following.
    (p -> q) ^ (r -> s) ^ [t -> ~(q V s) ^ t => (~p ^ ~r)
    note : the " ~ " sign means NOT,
    the " ^ " sign means AND,
    the " -> " sign means implies/conditional
    the " V " sign means OR
    the " => " sign means resultant or conclusion is.

    I've set up my working up to look like this.
    P -> q H1(Hypothesis 1)
    r -> s H2(Hypothesis 2)
    t -> ~(q V s) H3(Hypothesis 3)
    t H4(Hypothesis 4)
    _____________
    ~p ^ ~r C (Conclusion)

    Step one. I got H4 with H3 and AND both of them >> H4 ^ H3 which gives:

    t ^ [t -> ~(q V s)] and since t ^ t cancels out with the modus ponens rules it leaves us with ~(q V s).

    So now that H4 and H3 is gone we have H1 and H2 left. This is where i got stuck.

    I decided to use de morgan's law to simplify which gave me >> ~(q V s) => ~q ^ ~s and we can call this theory one (1).

    So far i've only got up to this part and now i'm stuck could you help me figured out what i need to do next?

    Working : t ^ [t -> ~(q V s)] <=> ~(q V s) H4 ^ H3
    <=> ~q ^ ~s (1).

    Next step = ? please help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Henderson's Avatar
    Joined
    Dec 2007
    Posts
    127
    Thanks
    2
    Your next step would be to use the Law of Contrapositives to change p -> q and r -> s into ~q -> ~p and ~s -> ~r.

    Since you know ~q ^ ~s already, you're a short step away from your goal.
    Nicely done so far!
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    15
    oh ok thnx alot let me try out the next step.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2008
    Posts
    15
    Damn... i suck bad...

    is (~p -> ~q) ^ (~q ^ ~s) possible? using the Hypothecial Syllogism concept. i know it works for if both of them are conditional but just wondering if this method works?

    if it does would it look something like ~p->~s or ~p^~s ._.

    if ~p->~s works out then... it would be alot easier because then i would just use Hypothetical syllgism law again for ~p->~s ^ ~s->~r which gives me ~p->~r but... then again it doesnt work out... sorry im really bad with this topic. a little more help please?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2008
    Posts
    15
    opps sorry its suppose to be ~q -> ~p not ~p -> ~q my bad.

    so that would mean :

    (~q -> ~p) ^ (~q ^ ~s) using exportation... is it possible?
    gives (~p ^ ~s) -> ~q ? ._. i don't know sorry =/
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2008
    Posts
    15
    Ok i think i got it but could someone check the answer for me? if i'm wrong let me know where i got wrong.

    t ^ [t -> ~(q V s)] <=> ~(q V s) ... H4 ^ H3 Modus ponens
    <=> ~q ^ ~s (1) ... de morgan's law

    p -> q => ~q -> ~p (2) ... Contrapositive
    r -> s => ~s -> ~r (3) ... Contrapositive

    (~q -> ~p) ^ (~q ^ ~s) .... (2) ^ (1)
    => ~p ^ ~s ... Disjunuctive Syllogism
    => ~s ^ ~p (4) ... Commutativity

    (~s -> ~r) ^ (~s ^ ~p) (3) ^ (4)
    => ~r ^ ~p ... Disjunctive Syllogism
    => ~p ^ ~r ... Commutativity <--- Conclusion
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Oct 2008
    Posts
    15
    opps i think i have the laws wrong... but could someone please check my answer? and let me know if i got it right or wrong... if wrong please show me where i went wrong.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Struggling to understand logic tables and proposition
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: October 24th 2011, 01:06 AM
  2. Replies: 2
    Last Post: October 4th 2011, 06:34 AM
  3. Logic problem
    Posted in the Math Challenge Problems Forum
    Replies: 6
    Last Post: December 4th 2010, 12:23 PM
  4. Proposition Help!?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 29th 2009, 03:16 PM
  5. Help on a problem to do with logic please
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: May 10th 2009, 12:10 AM

Search Tags


/mathhelpforum @mathhelpforum