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Math Help - another logic problem....PLEASE HELP

  1. #1
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    another logic problem....PLEASE HELP

    1. A -> X
    2. (A -> Y) -> (K v X)
    3. (A & X) -> Y
    4. ~K / X
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  2. #2
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    This one is hard.
    Again by indirect argument.
    1. A -> X
    2. (A -> Y) -> (K v X)
    3. (A & X) -> Y
    4. ~K / X
    5. Assume ~X
    6. ~A MT[1]
    7. (~K^~X)->~(A->Y) transposition[2]
    8. (~K^~X)->(A^~Y) negation[7]
    9. (~K^~X) conjunction [4,5]
    10 (A^~Y) MP[8,9]
    11 A simplification[10]
    12 (A^~A) conj. [11,6]
    There is the contradiction.
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