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Math Help - Help with the final step of a proof (valid argument)

  1. #1
    Junior Member
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    Sep 2010
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    Help with the final step of a proof (valid argument)

    I'm studying for a test and am doing some practice problems. I ran across this one in the Valid Arguments section. (I'll use ~ for the "not" symbol)

    Directions: Derive T

    (1) P --> Q
    (2) ~R --> ~Q
    (3) R --> S
    (4) P v T
    (5) ~S
    -----------------------------
    (6) ~R ......... (3)(5) Modus Tollens
    (7) ~Q ......... (2)(6) Modus Ponens
    (8) ~P...........(2)(7) Modus Tollens
    (9) ... This is where I'm stuck

    I can see that since ~P is true, then P must be false, and thus, to make P v T true, T must be true, but which "property" would I use?

    Sorry if this is a re-post. The internet froze up when I clicked the "submit new thread" button last time.
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  2. #2
    Junior Member
    Joined
    Oct 2006
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    Quote Originally Posted by Lprdgecko View Post
    I'm studying for a test and am doing some practice problems. I ran across this one in the Valid Arguments section. (I'll use ~ for the "not" symbol)

    Directions: Derive T

    (1) P --> Q
    (2) ~R --> ~Q
    (3) R --> S
    (4) P v T
    (5) ~S
    -----------------------------
    (6) ~R ......... (3)(5) Modus Tollens
    (7) ~Q ......... (2)(6) Modus Ponens
    (8) ~P...........(2)(7) Modus Tollens
    (9) ... This is where I'm stuck

    I can see that since ~P is true, then P must be false, and thus, to make P v T true, T must be true, but which "property" would I use?

    Sorry if this is a re-post. The internet froze up when I clicked the "submit new thread" button last time.
    If you have the rule version of disjunctive syllogism, then apply it to lines 4 and 8.
    If not, say what rules you do have (other than the rules you've already displayed).
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  3. #3
    Junior Member
    Joined
    Sep 2010
    Posts
    48
    Thanks for the answer. I just found it: Modus Tollendo Ponens.
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