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Homework Help: 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

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    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)
     
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