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Math Help - Symbolic Logic Proofs

  1. #1
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    Unhappy Symbolic Logic Proofs

    I need to construct a formal proof for the following valid arguments

    1) s -> (~a & b)
    ~s -> c
    a or ~b
    ____________
    c

    2) ~r
    ( b or c) -> r
    ~d or m
    d -> ~ ( c or p)
    _______________
    p -> m


    3) b -> c
    ~c
    (~b or ~p) -> s
    _______________
    s V q

    I been racking my brain for weeks on how to work these three problems, can anyone assist me?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tiago218 View Post
    I need to construct a formal proof for the following valid arguments

    1) s -> (~a & b)
    ~s -> c
    a or ~b
    ____________
    c
    i don't know what kind of logic/proofs you are studying, so i don't know how you want these set up, but here's the idea for this one.


    clearly s or ~s is true. if s is true, then we have ~a & b. however, this is the negation of a or ~b (DeMorgan's law), and so we cannot have that. thus, ~s must be true. but ~s => c, so that we can conclude c


    2) ~r
    ( b or c) -> r
    ~d or m
    d -> ~ ( c or p)
    _______________
    p -> m
    i don't think this is correct. are you sure there is no typo?

    3) b -> c
    ~c
    (~b or ~p) -> s
    _______________
    s V q
    we must show either s or q is true, perhaps both. since we have b => c and ~c, then we have ~b. if ~b is true, then ~b or ~p is true. and hence, the last implication says s is true. if s is true, then s or q is true, and we conclude accordingly.


    i leave the formal proofs to you
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