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?