Question 1179563
**Problem 1:**

1. N ≡ F  (Given)
2. ~F v ~N  (Given)
3. D ⊃ N  (Given)
4. | F v D  (Assumption for Indirect Proof)
5. | | F  (Assumption for v Elimination)
6. | | N  (1, 5, ≡ Elimination)
7. | | N v ~D  (6, v Introduction)
8. | | ~D  (2, 7, v Elimination)
9. | | F ⊃ ~D  (5, 8, ⊃ Introduction)
10. | | D  (Assumption for v Elimination)
11. | | N  (3, 10, ⊃ Elimination)
12. | | N v ~D  (11, v Introduction)
13. | | ~D  (2, 12, v Elimination)
14. | | D ⊃ ~D  (10, 13, ⊃ Introduction)
15. | | ~D v ~D  (4, 9, 14, v Elimination)
16. | | ~D  (15, Tautology)
17. | ~(F v D)  (4, 16, ⊃ Introduction) 

**Problem 2:**

1. M ⊃ (∼B ⊃ J)  (Given)
2. B ⊃ (~M * ~M)  (Given)
3. ∼J  (Given)
4. | M  (Assumption for Indirect Proof)
5. | | ∼B  (Assumption for Indirect Proof) 
6. | | ∼B ⊃ J (1, 4, ⊃ Elimination)
7. | | J  (5, 6, ⊃ Elimination)
8. | | J * ~J  (3, 7, * Introduction)
9. | B  (5, 8, ~ Introduction)
10. | ~M * ~M  (2, 9, ⊃ Elimination)
11. | ~M  (10, * Elimination)
12. | M * ~M  (4, 11, * Introduction)
13. ~M  (4, 12, ~ Introduction)

**Problem 3:**

1. ~X ⊃ ~~O  (Given)
2. ~X ⊃ A  (Given)
3. ~(O * A)  (Given)
4. | ~X  (Assumption for Indirect Proof)
5. | ~~O  (1, 4, ⊃ Elimination)
6. | O  (5, ~~ Elimination)
7. | A  (2, 4, ⊃ Elimination)
8. | O * A  (6, 7, * Introduction)
9. | (O * A) * ~(O * A)  (3, 8, * Introduction)
10. X  (4, 9, ~ Introduction)