Sentential Calculus Problems

1.  {1} 1. (P v Q)-> (R & S)       P
    {2} 2. -R                       P          / -Q

2.  {1} 1. P -> Q                   P
    {2} 2. -P -> R                  P         / Q v R

3.  {1} 1. (Q & R) -> P                P
    {2} 2. (R -> P) -> S               P
    {3} 3. Q                           P        / S

4.  {1} 1. P v (Q & R)                 P
    {2} 2. (P v Q) -> S                P       / R v S

5.  {1} 1. P -> (Q -> R)              P
    {2} 2. P & -R                     P        / -Q

6.  {1} 1. (G & L) v (W & T)          P
    {2} 2. -G                         P        / T

7.  {1} 1. (P & Q) & R                  P
    {2} 2. (Q <-> R) -> (S v T)         P       / T v S

8.  {1} 1. (P & Q) -> R             P
    {2} 2. (P -> R) -> S            P
    {3} 3. -Q v T                   P         / Q -> (S & T)

9.  {1} 1. (S -> -P) & (P -> Q)     P
    {2} 2. Q -> S                   P
    {3} 3. -R -> P                  P   / R

10. {1} 1. S -> (T -> P)        P
    {2} 2. P -> -P              P
    {3} 3. (Q -> S) & (R -> T)  P      / Q -> -R

11. {1} 1. P -> (Q -> R)       P
    {2} 2. P -> (S -> T)       P
    {3} 3. P & (Q v S)         P
    {4} 4. -R                  P      / T

12. {1} 1. P -> (Q -> -P)           P
    {2} 2. P <-> Q                  P    / -P & -Q

13. {1} 1. P & (Q v R)               P
    {2} 2. (P & R) -> -(S v T)       P
    {3} 3. (-S v -T) -> -(P & Q)     P     / S <-> T

14. {1} 1. P v (-Q v P)         P
    {2} 2. Q v (-P v Q)         P     / (P & Q) v (-P & -Q)

15. {1} 1. (P v Q) v (R & S)              P
    {2} 2. (-P & S) & -(-P & Q)           P   / -P & R

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