1. A->X

2. (A->Y)->(K v X)

3. (A & X)->Y

4. ~K/ X

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- Oct 21st 2007, 08:40 AMambergarrett955another logic problem....PLEASE HELP
1. A

**->**X

2. (A**->**Y)**->**(K v X)

3. (A & X)**->**Y

__4. ~K__/ X - Oct 21st 2007, 10:48 AMPlato
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.