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In the case of a contradicted conditional given:

  1. Oct 2, 2014 #1
    1. The problem statement, all variables and given/known data
    If I have a given in a proof in the form:
    A or B or C ... etc. etc. and if I choose to approach this given in a case by case basis: (assuming one of the A,B,C... one at a time) and if one or more of the assumptions contradicts some other given in the proof does that mean that I can simply ignore that possibility?


    2. Relevant equations


    3. The attempt at a solution

    For example: if A or B or C

    case1: Assume A
    Contradiction
    Therefore B or C

    I was under the impression that in order for a case-by-case proof to suceed you need to ensure that all the possible cases come out to be true, however what about this situation:

    Assume not A

    A or B or C
    case1: A
    However, not A, contradiction

    case 2: B
    ...
    Goal is true
    case 3: C
    ...
    Goal is true
     
  2. jcsd
  3. Oct 2, 2014 #2

    vela

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    Are you talking about a statement like: If A or B or C, then D? To show that statement is true, you need to show A→D, B→D, and C→D.

    You can't infer that if A is false, then B or C is true. It's possible for A, B, and C to all be false, right?
     
  4. Oct 2, 2014 #3

    LCKurtz

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    I think he might be thinking Given (A or B or C) and not(A) then B or C.
     
  5. Oct 6, 2014 #4
    Kurtz is correct, the given would be of a form
    (A or B or C)
    Though it doesn't have to have three possibilities, it could have as arbitrarily many, it doesn't really matter for the sake of this discussion, just as long as there are 2 or more.
     
  6. Oct 6, 2014 #5

    RUber

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    You do need to ensure that each case comes out true. That means that ( A or B or C) can be made true in each case. If you are given A is false, you will not have a case where you assume A is true.

    Normally if you have n statements, you will have ##2^n## possible combinations of T/F in a truth table. Constraints such as A is false simply reduce the number of potential cases to look at. Now there are only ##2^2## combinations to consider. Only one of which makes the first statement (A or B or C) false.
     
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