# Logic

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Can someone please help me solve these problems? I have to use the 17 rules of inference to prove the arguments valid:

1) 1. T = R
2. (~R > ~T) > (P . ~S) / ~S v T

2) 1. C > F
2. A > B
3. ~F . A
4. ~C > (B > D) / B . D

3) 1. (S v Q) / ~P > ~S

4) 1. D > P /(I . D) > P

5) 1. P v (Y . H)
2. (P v Y) > ~(H v C)
3. (P . ~C) > (K . X) / X v T

6) 1. A = J
2. A v J
3. A > (J > W) / W

7) 1. P v R
2. ~P v (Q . R)
3. R > (Q . S) / Q . S

8) 1. ~(R v S)
2. ~(M . N) > (O v P)
3. ~[O v (N . P)]
4. N = ~(Q . R) / ~(M v O)

9) 1. (J > K) . (~O > ~P)
2. (L > J) . (~M > ~O)
3. ~K > (L v ~M)
4. ~K . G / ~P

10) 1. (L v P) > U
2. (M > U) > I
3. P / I

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