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Math Help - Symbolic Argument, Find valid conclusion and justify.

  1. #1
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    Symbolic Argument, Find valid conclusion and justify.

    It's me again, lol.

    Find a valid conclusion to the argument given bwlow in symbolic form. Justify your answer.

    ~p (p^ ~q) ------ premise 1
    q --> r --------- premise 2
    ~ r -------------- premise 3
    -----------------------------------------
    therefore, ?

    Here is what I did last night,

    1. ~r PIII
    2. ~r-->~q PII, contrapositive
    3. ~q 1,2,detachment
    4. ~p v q PI, DeMorgan's Laws
    5. ~p 3,4,disjunctive syllogism

    therefore, ~p. not sure if this is right or my work is right, thanks in advance.
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  2. #2
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    Quote Originally Posted by stueycal View Post
    Find a valid conclusion to the argument given bwlow in symbolic form. Justify your answer.
    ~p (p^ ~q) ------ premise 1
    q --> r --------- premise 2
    ~ r -------------- premise 3
    Look at premise 1.
    It does not seem to be correct.
    Please correct it.
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  3. #3
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    ~(p^ ~q) ------ premise 1
    q --> r --------- premise 2
    ~ r -------------- premise 3

    whoops.
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  4. #4
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    Quote Originally Posted by stueycal View Post
    ~(p^ ~q) ------ premise 1
    q --> r --------- premise 2
    ~ r -------------- premise 3
    Premises 2&3 give \neg q by Modus Tollens.
    From premise 1 and DeMorgan's Theorem we get \neg p \vee q .
    Then by Disjunctive Syllogism we get \neg p.
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