Hello, I am stuck trying to figure this Symbolic Logic problem out. I'm using the rules of inference and replacement rules. I've taken it two different ways, and became stuck on both of these.

Key:

~ : Negation

⊃ : IF THEN

* : And

v : Or

= : Bi-conditional statement

Here is what I have so far.

1. ~B⊃ ~(s*t)

2. ~s= ( p v o )

3. ~(p v ( ~ t v o ))

4. ~A ⊃ p // A*B

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5. [(~s ⊃ (p v o)) * (( p v o ) ⊃ ~ s )] 2 Bi-conditional Exchange

6.~s⊃ ( p v o ) 5 Simp

7. (p v o ) ⊃ ~ s 5 Simp

8. p * o 7 Demorgans

9. p 8 Simp

10. ~ A .4 Motus Ponens

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Here is what a a class mate finished with. His looks right, but with all the negations, I tend to lose track of all the negatives.

Same first 4 Lines.

5. ~B v ~ ( S * T ) 1 CE

6. ~B v (~ S v ~ T) 5 DeM

7. (( ~ S ⊃ ( P v O )) * ((P v O) ⊃ ~S) BE

8. ~ S ⊃ ( P v O ) 7 Simp

9. (P v O) ~ S 7 Simp

10. ~~ S v ( P v O) 8 Conditional Exchange

11.~( P v O) v ~ S 9 Conditional Exchange

12. ~ P v ~( T v O) 3 Dem

13. ~~ A v P 4 Dem

14. A v P 13 Double Negation

15. S v ( P v O ) 10 Double Negation

16. (~ P * ~ O) v ~ S 11 DeM

17. ~ B * ( ~ S v ~ T ) 6 DeM

18. ~ B 17 Simp

19. ( ~ S v ~ T ) 17 Simp

20. A * P 14 Dem

21. A 20 Simp

22. P 20 Simp

23. ~~ (T v O ) 12,22 DS

24. ( T v O ) 23 DN

25. T * O 24 DEM

26. T 25 Simp

27. O 25 Simp

28. ~ B * (~ S * ~ T ) 17 DEM

29. B 1,28 MT

30. A * B 21, 29 Conjunction.

Is this one correct?