can anyone solve these proofs? Thanks in advance..
1. A v B
2. C
3. (A & C) > D
4. ~(~F & B) :. D v F
1. ~(A & B) = ~C
2. (D v E) > C :. E > A
The = is the triple bar
1. A v B
2. C
3. (A & C) > D
4. ~(~F & B) :. D v F
1. ~(A & B) = ~C
2. (D v E) > C :. E > A
The = is the triple bar
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1. A v B Premise
2. C Premise
3. (A & C) > D Premise
4. ~(~F & B) Premise
5. (C & A) > D 3 Commutation
6. C > (A > D) 5 Exportation
7. A > D 2,6 Modus Ponens
8. ~(B & ~F) 4 Commutation
9. ~B v ~~F 8 De Morgan's Law
10. ~B v F 9 Double Negation
11. B > F 10 Implication
12. (A > D) & (B > F) 7,11 Conjunction
13. D v F 1,12 Dilemma
1. ~(A & B) <> ~C Premise
2. (D v E) > C Premise
3. (~(A & B) > ~C) & (~C > ~(A & B)) 1 Equivalence
4. ~(A & B) > ~C 3 Simplification
5. C > (A & B) 4 Transposition
6. (D v E) > (A & B) 2,5 Hypothetical Syllogism
7. ~(D v E) v (A & B) 6 Implication
8. (~(D v E) v A) & (~(D v E) v B) 7 Distribution
9. ~(D v E) v A 8 Simplification
10. A v ~(D v E) 9 Commutation
11. A v ~(E v D) 10 Commutation
12. A v (~E & ~D) 11 De Morgan's Law
13. (A v ~E) & (A v ~D) 12 Distribution
14. A v ~E 13 Simplification
15. ~E v A 14 Commutation
16. E > A 15 Implication
2. C Premise
3. (A & C) > D Premise
4. ~(~F & B) Premise
5. (C & A) > D 3 Commutation
6. C > (A > D) 5 Exportation
7. A > D 2,6 Modus Ponens
8. ~(B & ~F) 4 Commutation
9. ~B v ~~F 8 De Morgan's Law
10. ~B v F 9 Double Negation
11. B > F 10 Implication
12. (A > D) & (B > F) 7,11 Conjunction
13. D v F 1,12 Dilemma
1. ~(A & B) <> ~C Premise
2. (D v E) > C Premise
3. (~(A & B) > ~C) & (~C > ~(A & B)) 1 Equivalence
4. ~(A & B) > ~C 3 Simplification
5. C > (A & B) 4 Transposition
6. (D v E) > (A & B) 2,5 Hypothetical Syllogism
7. ~(D v E) v (A & B) 6 Implication
8. (~(D v E) v A) & (~(D v E) v B) 7 Distribution
9. ~(D v E) v A 8 Simplification
10. A v ~(D v E) 9 Commutation
11. A v ~(E v D) 10 Commutation
12. A v (~E & ~D) 11 De Morgan's Law
13. (A v ~E) & (A v ~D) 12 Distribution
14. A v ~E 13 Simplification
15. ~E v A 14 Commutation
16. E > A 15 Implication