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Discrete math:propositional logic

  1. Oct 10, 2009 #1
    1. The problem statement, all variables and given/known data
    I want to construct a truth table for the following propositions


    2. Relevant equations

    (a) ¬p ∨ q
    (b) p ∧ q ⇒ p
    (c) ¬p ∨ q ⇔ p ⇒ q



    3. The attempt at a solution

    Approach:
    1) Determine the order of precedence:

    2) Fill in the values for the operator with the higher precedence:


    3) Next fill in the values for the lower precedence

    I guess, answer for a , b and c is:

    (a) ¬p ∨ q
    p q ¬p ∨q
    t t f t
    t f f f
    f t t t
    f f t t

    (b) p ∧ q ⇒ p
    p q p ∧ q ⇒ p
    t t t t
    t f f t
    f t f t
    f f f t

    (c) ¬p ∨ q ⇔ p ⇒ q
    p q ¬p ∨q ⇔ p ⇒ q
    t t f t t t
    t f f f t f
    f t t t t t
    f f t t t t

    Is this right?

    Further, can anyone explain intuitive statements to explain any of the above--say (a) and (b)---i.e reasoning out (a) and (b) truth table through example statements
    1. The problem statement, all variables and given/known data

    please help!!!!

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 10, 2009 #2
    Your tables are not clear enough for me to make out exactly what you are doing. I'm also not convinved there is a precedence rule between [itex]\Rightarrow[/itex] and [itex]\Leftrightarrow[/itex]. Part (c) may end up being ambiguous.

    --Elucidus
     
  4. Oct 11, 2009 #3
    Can you comment upon part (a) and (b) only at least?
    (a) ¬p ^ q
    p q ¬p ^q
    t t f t
    t f f f
    f t t t
    f f t t


    (b) p ¬ q => p
    p q p ¬ q => p
    t t t t
    t f f t
    f t f t
    f f f t

    Can you give statements t prove the logic?Or making it independent of precedence, srating from a scratch, how would you go about?
     
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