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Question 1209921: A. Use the first thirteen rules of inference to derive the conclusions of the following symbolized arguments:
1. (O v M) ⊃ S
2. ~S / ~M
1. ~(~E • ~N) ⊃ T
2. G ⊃ (N v E) /G ⊃ T
1. ~(F • A)
2. ~(L v ~A)
3. D ⊃ (F v L) /~D
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! 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**
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