Question 1209921
You've asked for the derivations again, and they're the same as before. Here they are, with the rules of inference clearly labeled:

**Argument 1:**

1.  (O v M) ⊃ S
2.  ~S / ~M

3.  ~(O v M)  **Modus Tollens (MT), 1, 2**
4.  ~O • ~M  **De Morgan's Theorem (DeM), 3**
5.  ~M  **Simplification (Simp), 4**

**Argument 2:**

1.  ~(~E • ~N) ⊃ T
2.  G ⊃ (N v E) / G ⊃ T

3.  N v E  **Double Negation (DN), ~(~E • ~N)**
4.  G ⊃ ~(~E • ~N) **Hypothetical Syllogism (HS), 2, 3**
5.  G ⊃ T  **Hypothetical Syllogism (HS), 4, 1**

**Argument 3:**

1.  ~(F • A)
2.  ~(L v ~A)
3.  D ⊃ (F v L) / ~D

4.  ~L • ~~A  **De Morgan's Theorem (DeM), 2**
5.  ~L • A  **Double Negation (DN), 4**
6.  A  **Simplification (Simp), 5**
7.  ~F v ~A  **De Morgan's Theorem (DeM), 1**
8.  ~F  **Disjunctive Syllogism (DS), 6, 7**
9.  ~L  **Simplification (Simp), 5**
10. F v L  **Addition (Add), 8, 9**
11. ~D  **Modus Tollens (MT), 3, 10**