Results 1 to 2 of 2

Math Help - Symbolic Logic Proof Help

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    1

    Symbolic Logic Proof Help

    1. (P⋅G) ⊃ R
    2. (R⋅S) ⊃ T
    3. P⋅S
    4. G v R

    The conclusion is R v T.

    I don't even know where to start and I can use basic rules of inference (MT, Disjunctive Syllogism, Dilemma, etc.) and replacement rules (Contraposition, Commutation, etc.).

    Any help would be appreciated!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,615
    Thanks
    1578
    Awards
    1
    Quote Originally Posted by joejoejohnson View Post
    1. (P⋅G) ⊃ R
    2. (R⋅S) ⊃ T
    3. P⋅S
    4. G v R
    The conclusion is R v T.
    I would prove this by contradiction.
    Suppose it is not true.
    \begin{gathered}<br />
  5.\neg R \cdot \neg T \hfill \\<br />
  6.\neg P \vee \neg G,\,1 \hfill \\<br />
  7.\neg R \vee \neg S,\,2 \hfill \\<br />
  8.\neg R,\,5 \hfill \\<br />
  9.G,\,4,8 \hfill \\<br />
  10.\neg \neg G,\,9 \hfill \\<br />
  11.\neg P,\,6,10 \hfill \\<br />
  12.P,\,3 \hfill \\<br />
  13.P \cdot \neg P,\,12,11 \hfill \\ <br />
\end{gathered}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Conceptual Questions for Modern Symbolic Logic
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: December 11th 2011, 10:56 AM
  2. Symbolic Logic Help
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: April 9th 2010, 01:25 AM
  3. Symbolic Logic Proofs
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 13th 2009, 07:56 PM
  4. Symbolic Logic Problem (Urgent)
    Posted in the Math Topics Forum
    Replies: 8
    Last Post: December 13th 2008, 11:27 PM
  5. Symbolic Logic help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 11th 2008, 03:56 AM

Search Tags


/mathhelpforum @mathhelpforum