Results 1 to 3 of 3

Math Help - Logical Equivalence Help

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    5

    Logical Equivalence Help

    Hello, I have a problem in my computer science class that goes as follows:

    " prove the following using logical proofs (not truth tables)"

    (p --> q) V (p --> r) V p is a tautology

    I can get a few steps into it, then get stuck. Please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,383
    Thanks
    1474
    Awards
    1
    Quote Originally Posted by triathlete View Post
    Hello, I have a problem in my computer science class that goes as follows:

    " prove the following using logical proofs (not truth tables)"

    (p --> q) V (p --> r) V p is a tautology

    I can get a few steps into it, then get stuck. Please help!
    \begin{gathered}<br />
  \left( {p \to q} \right) \vee \left( {p \to r} \right) \vee p \hfill \\<br />
  \left( {\neg p \vee q} \right) \vee \left( {\neg p \vee r} \right) \vee p \hfill \\<br />
  \neg p \vee \left( {q \vee r} \right) \vee p \hfill \\<br />
  \left( {\neg p \vee p} \right) \vee \left( {q \vee r} \right) \hfill \\ <br />
\end{gathered}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Sep 2009
    Posts
    502
    By predicate calculus:

    P (hypothesis)

    P\vee (P\rightarrow R) (Disjunction Introduction)

    (P\vee (P\rightarrow R))\vee (P\rightarrow Q) (Disjunction Introduction and end of proof)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Logical equivalence
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: November 12th 2011, 05:22 PM
  2. [SOLVED] need to check logical equivalence
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: September 5th 2011, 10:49 PM
  3. Logical Equivalence
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: October 22nd 2010, 01:43 AM
  4. Proving Logical equivalence
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 25th 2009, 10:35 AM
  5. Logical Equivalence
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 23rd 2008, 08:17 PM

Search Tags


/mathhelpforum @mathhelpforum