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Math Help - Logic problems

  1. #1
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    Logic problems

    Hello there!
    I have 3 tasks to solve, and I believe that I've achieved correct answer, but I might be totally wrong.

    The question is if these expressions are correct or incorrect (true/false)

    a) C -> (A -> B) |= -C ^ (-A v B)

    b) C -> A( -> B) |= -C v -A v B

    c) -C v (-A v B) |= C->(A->B)


    I'd appreciate your help, and solutions for these tasks.

    /David.T
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  2. #2
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    Recall that -A \/ B is equivalent to A -> B and try rewriting the formulas you are given using this equivalence as much as possible.
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  3. #3
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    for task a)
    A = 1, B = 1, C = 1

    LEFT: 1 -> (1 -> 1) gives 1 -> 1 gives 1

    RIGHT: 0 ^ (0 v 1) gives 0 ^ 1 gives 0

    1 =| 0 must be incorrect/false?
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  4. #4
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    do you not have any proof methods e.g semantic tableau that you can use?
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  5. #5
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    for task a)
    A = 1, B = 1, C = 1

    LEFT: 1 -> (1 -> 1) gives 1 -> 1 gives 1

    RIGHT: 0 ^ (0 v 1) gives 0 ^ 1 gives 0

    1 |= 0 must be incorrect/false?
    Yes.
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  6. #6
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    can we not just simply draw up three tableau's for these to show if they are true or if not find a model using the tableau?
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