Question 1179864
Let's break down each argument step-by-step using ordinary proofs:

**1) Argument:**

1.  I v (N • F)
2.  I ⊃ F / F

**Proof:**

3.  ~I ∨ F  (2, Implication)
4.  I ∨ (N • F) (1, Copy)
5.  ~I ∨ F  (3, Copy)
6.  F ∨ ~I (5, Commutation)
7.  F ∨ (N • F) (4, Resolution, 6)
8.  F ∨ (N • F) (7, Copy)
9.  F ∨ N (8, Distribution)
10. F (9, Simplification)

**Therefore, F is proven.**

**2) Argument:**

1.  P ⊃ ~M
2.  C ⊃ M
3.  ~L v C
4.  (~P ⊃ ~E) • (~E ⊃ ~C)
5.  P v ~P / ~L

**Proof:**

6.  ~P ∨ ~M (1, Implication)
7.  ~C ∨ M (2, Implication)
8.  ~P ⊃ ~E (4, Simplification)
9.  ~E ⊃ ~C (4, Simplification)
10. P ∨ ~P (5, Copy)
11. P (10, Tautology)
12. ~M (6, 11, Modus Ponens)
13. ~C (7, 12, Modus Tollens)
14. ~L (3, 13, Disjunctive Syllogism)

**Therefore, ~L is proven.**

**3) Argument:**

1.  O ⊃ (Q • N)
2.  (N ∨ E) ⊃ S / O ⊃ S

**Proof:**

3.  ~O ∨ (Q • N) (1, Implication)
4.  N ∨ E ⊃ S (2, Copy)
5.  ~O ∨ Q (3, Simplification)
6.  ~O ∨ N (3, Simplification)
7.  N ∨ E (6, Addition)
8.  S (4, 7, Modus Ponens)
9.  ~O ∨ S (6, 8, Hypothetical Syllogism)
10. O ⊃ S (9, Implication)

**Therefore, O ⊃ S is proven.**