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Math Help - Help with a few propositional logic proofs

  1. #1
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    Help with a few propositional logic proofs

    I'm having a really hard time solving the following proofs in Tomassi's Logic book.

    1)
    P v Q : (P v R) -> (P v(Q & R))

    2)
    P : Q -> (P <->Q)

    3)

    P v (Q v R) : Q v (P v R)
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  2. #2
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    Quote Originally Posted by unprocessed9 View Post
    I'm having a really hard time solving the following proofs in Tomassi's Logic book.
    1) P v Q : (P v R) -> (P v(Q & R))
    Please explain what the notation means and what are you to do with it.
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  3. #3
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    I have to prove the proofs using steps and specific notations (used in the Tomassi Book)
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  4. #4
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    Quote Originally Posted by unprocessed9 View Post
    (used in the Tomassi Book)
    I for one have never heard of Tomassi much less his textbook (I taught logic many times).
    It would be shear accident if anyone here knows the notation used in a particular text.
    So if you want help with this, you are going have to type out the list of rules and notations used in that text.
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  5. #5
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    Quote Originally Posted by Plato View Post
    I for one have never heard of Tomassi much less his textbook (I taught logic many times).
    It would be shear accident if anyone here knows the notation used in a particular text.
    So if you want help with this, you are going have to type out the list of rules and notations used in that text.
    & And
    &I And Introduction

    v Or
    (vE) Or Elimination
    (vI) Or Introductioni

    -> If…then
    ->I
    ->E

    <-> If and only if

    ~ Not


    There are also rules of assuming for the antecedent of a conditional (assumption cp), and assumption for part of an 'or' statement (assumption vE)
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  6. #6
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    Quote Originally Posted by unprocessed9 View Post
    I'm having a really hard time solving the following proofs in Tomassi's Logic book.

    1)
    P v Q : (P v R) -> (P v(Q & R))

    2)
    P : Q -> (P <->Q)

    3)

    P v (Q v R) : Q v (P v R)
    Assuming that : means equivalent then No 3 can be solved in the following way:


    P v (Q v R) = (P v Q)v R =.................................. ( by associativity)

    =(Q v P)v R = .................................................. ..(By commutativity)

    =Q v (P v R) .................................................. ......(BY associativity again).


    Do you want the rest of the problems solved in this way??
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