1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

DISCRETE MATH: Which of these compound propositions is satisfiable? No use truthtable

  1. Jan 17, 2007 #1
    1. The problem statement, all variables and given/known data

    Is this compound statement satisfiable?

    [tex](p\,\vee\,q\,\vee\,\neg\,r)\,\wedge\,(p\,\vee\,\neg\,q\,\vee\,\neg\,s)\,\wedge\,(p\,\vee\,\neg\,r\,\vee\,\neg\,s)\,\wedge\,(\neg\,p\,\vee\,\neg\,q\,\vee\,\neg\,s)\,\wedge\,(p\,\vee\,q\,\vee\,\neg\,s)[/tex]


    2. Relevant equations

    I guess you are supposed to use the following instead of truth tables somehow:

    Logical equivalences - Domination, Idempotent, Double negation, Commutative, De Morgan's, Absorption, Negation, Associate, Distributive.


    3. The attempt at a solution

    I "converted" the first term in the expression:

    [tex](p\,\vee\,q\,\vee\,\neg\,r)\,\equiv\,\left[(\neg\,p\,\longrightarrow\,q)\,\vee\,\neg\,r\right][/tex]

    Now what do I do though?
     
  2. jcsd
  3. Jan 18, 2007 #2
    I figured it out!

    It was simple.

    The equation is satifiable.

    Set p = TRUE and q = FALSE. Since it is all OR logical connectives, it was simple to find these values which make the statement true.
     
  4. Jan 18, 2007 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    I really hope you didn't just try things at random. Just use those laws above. It is quite straight forward.
     
  5. Mar 12, 2010 #4
    Re: DISCRETE MATH: Which of these compound propositions is satisfiable? No use trutht

    can you "VinnyCee" answer this with some explanations

    *Is this compound statment is satisfiable/why?


    (b) (¬p ∨ ¬q ∨ r) ∧ (¬p ∨ q ∨ ¬s) ∧ (p ∨ ¬q ∨ ¬s) ∧
    (¬p ∨ ¬r∨ ¬s)∧ (p ∨ q ∨ ¬r)(¬p ∨ ¬r∨ s)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: DISCRETE MATH: Which of these compound propositions is satisfiable? No use truthtable
  1. Compound Propositions (Replies: 2)

Loading...